id sid tid token lemma pos ejpam-3086 1 1 european european PROPN ejpam-3086 1 2 journal journal PROPN ejpam-3086 1 3 of of ADP ejpam-3086 1 4 pure pure ADJ ejpam-3086 1 5 and and CCONJ ejpam-3086 1 6 applied apply VERB ejpam-3086 1 7 mathematics mathematic NOUN ejpam-3086 1 8 vol vol NOUN ejpam-3086 1 9 . . PROPN ejpam-3086 2 1 10 10 NUM ejpam-3086 2 2 , , PUNCT ejpam-3086 2 3 no no INTJ ejpam-3086 2 4 . . NOUN ejpam-3086 2 5 5 5 NUM ejpam-3086 2 6 , , PUNCT ejpam-3086 2 7 2017 2017 NUM ejpam-3086 2 8 , , PUNCT ejpam-3086 2 9 946 946 NUM ejpam-3086 2 10 - - SYM ejpam-3086 2 11 954 954 NUM ejpam-3086 2 12 issn issn PROPN ejpam-3086 2 13 1307 1307 NUM ejpam-3086 2 14 - - SYM ejpam-3086 2 15 5543 5543 NUM ejpam-3086 2 16 – – PUNCT ejpam-3086 2 17 www.ejpam.com www.ejpam.com X ejpam-3086 2 18 published publish VERB ejpam-3086 2 19 by by ADP ejpam-3086 2 20 new new PROPN ejpam-3086 2 21 york york PROPN ejpam-3086 2 22 business business PROPN ejpam-3086 2 23 global global ADJ ejpam-3086 2 24 harmonic harmonic PROPN ejpam-3086 2 25 and and CCONJ ejpam-3086 2 26 ( ( PUNCT ejpam-3086 2 27 φ φ PROPN ejpam-3086 2 28 , , PUNCT ejpam-3086 2 29 φ́)-holomorphic φ́)-holomorphic ADJ ejpam-3086 2 30 maps map NOUN ejpam-3086 2 31 on on ADP ejpam-3086 2 32 some some DET ejpam-3086 2 33 generalization generalization NOUN ejpam-3086 2 34 of of ADP ejpam-3086 2 35 contact contact NOUN ejpam-3086 2 36 metric metric ADJ ejpam-3086 2 37 manifolds manifold NOUN ejpam-3086 2 38 fereshteh fereshteh NOUN ejpam-3086 2 39 malek1 malek1 NOUN ejpam-3086 2 40 , , PUNCT ejpam-3086 2 41 mahboobeh mahboobeh NOUN ejpam-3086 2 42 samanipour2,∗ samanipour2,∗ NOUN ejpam-3086 2 43 1 1 NUM ejpam-3086 2 44 faculty faculty NOUN ejpam-3086 2 45 of of ADP ejpam-3086 2 46 mathematics mathematic NOUN ejpam-3086 2 47 , , PUNCT ejpam-3086 2 48 k. k. PROPN ejpam-3086 2 49 n. n. PROPN ejpam-3086 2 50 toosi toosi PROPN ejpam-3086 2 51 university university PROPN ejpam-3086 2 52 of of ADP ejpam-3086 2 53 technology technology PROPN ejpam-3086 2 54 , , PUNCT ejpam-3086 2 55 tehran tehran PROPN ejpam-3086 2 56 , , PUNCT ejpam-3086 2 57 iran iran PROPN ejpam-3086 2 58 2 2 NUM ejpam-3086 2 59 department department NOUN ejpam-3086 2 60 of of ADP ejpam-3086 2 61 mathematics mathematic NOUN ejpam-3086 2 62 , , PUNCT ejpam-3086 2 63 payame payame NOUN ejpam-3086 2 64 noor noor PROPN ejpam-3086 2 65 university university PROPN ejpam-3086 2 66 , , PUNCT ejpam-3086 2 67 p.o.box.19395 p.o.box.19395 PROPN ejpam-3086 2 68 - - PUNCT ejpam-3086 2 69 3697 3697 NUM ejpam-3086 2 70 , , PUNCT ejpam-3086 2 71 tehran tehran PROPN ejpam-3086 2 72 , , PUNCT ejpam-3086 2 73 iran iran PROPN ejpam-3086 2 74 abstract abstract ADJ ejpam-3086 2 75 . . PUNCT ejpam-3086 3 1 we we PRON ejpam-3086 3 2 study study VERB ejpam-3086 3 3 ( ( PUNCT ejpam-3086 3 4 φ φ PROPN ejpam-3086 3 5 , , PUNCT ejpam-3086 3 6 φ́)-holomorphic φ́)-holomorphic ADJ ejpam-3086 3 7 and and CCONJ ejpam-3086 3 8 harmonic harmonic ADJ ejpam-3086 3 9 maps map NOUN ejpam-3086 3 10 on on ADP ejpam-3086 3 11 almost almost ADV ejpam-3086 3 12 contact contact NOUN ejpam-3086 3 13 metric metric ADJ ejpam-3086 3 14 manifolds manifold NOUN ejpam-3086 3 15 satisfying satisfy VERB ejpam-3086 3 16 dη dη NOUN ejpam-3086 3 17 + + CCONJ ejpam-3086 3 18 dηoφ dηoφ PROPN ejpam-3086 3 19 ⊗ ⊗ PROPN ejpam-3086 3 20 φ φ PROPN ejpam-3086 3 21 = = SYM ejpam-3086 3 22 2φ 2φ NUM ejpam-3086 3 23 . . PUNCT ejpam-3086 4 1 it it PRON ejpam-3086 4 2 should should AUX ejpam-3086 4 3 be be AUX ejpam-3086 4 4 noted note VERB ejpam-3086 4 5 that that SCONJ ejpam-3086 4 6 these these DET ejpam-3086 4 7 manifolds manifold NOUN ejpam-3086 4 8 are be AUX ejpam-3086 4 9 not not PART ejpam-3086 4 10 necessarily necessarily ADV ejpam-3086 4 11 contact contact VERB ejpam-3086 4 12 metric metric ADJ ejpam-3086 4 13 manifolds manifold NOUN ejpam-3086 4 14 . . PUNCT ejpam-3086 5 1 examples example NOUN ejpam-3086 5 2 of of ADP ejpam-3086 5 3 such such ADJ ejpam-3086 5 4 manifolds manifold NOUN ejpam-3086 5 5 are be AUX ejpam-3086 5 6 nearly nearly ADV ejpam-3086 5 7 sasakain sasakain ADJ ejpam-3086 5 8 and and CCONJ ejpam-3086 5 9 quasi quasi ADJ ejpam-3086 5 10 contact contact NOUN ejpam-3086 5 11 metric metric ADJ ejpam-3086 5 12 manifolds manifold NOUN ejpam-3086 5 13 . . PUNCT ejpam-3086 6 1 2010 2010 NUM ejpam-3086 6 2 mathematics mathematic NOUN ejpam-3086 6 3 subject subject NOUN ejpam-3086 6 4 classifications classification NOUN ejpam-3086 6 5 : : PUNCT ejpam-3086 6 6 53c40 53c40 NUM ejpam-3086 6 7 , , PUNCT ejpam-3086 6 8 53c15 53c15 NUM ejpam-3086 6 9 , , PUNCT ejpam-3086 6 10 53c25 53c25 NUM ejpam-3086 6 11 key key ADJ ejpam-3086 6 12 words word NOUN ejpam-3086 6 13 and and CCONJ ejpam-3086 6 14 phrases phrase NOUN ejpam-3086 6 15 : : PUNCT ejpam-3086 6 16 quasi quasi NOUN ejpam-3086 6 17 contact contact NOUN ejpam-3086 6 18 metric metric PROPN ejpam-3086 6 19 manifold manifold ADJ ejpam-3086 6 20 , , PUNCT ejpam-3086 6 21 nearly nearly ADV ejpam-3086 6 22 sasakian sasakian ADJ ejpam-3086 6 23 manifold manifold NOUN ejpam-3086 6 24 , , PUNCT ejpam-3086 6 25 quasi quasi ADJ ejpam-3086 6 26 kähler kähler PROPN ejpam-3086 6 27 manifold manifold PROPN ejpam-3086 6 28 , , PUNCT ejpam-3086 6 29 holomorphic holomorphic ADJ ejpam-3086 6 30 map map NOUN ejpam-3086 6 31 , , PUNCT ejpam-3086 6 32 contact contact NOUN ejpam-3086 6 33 metric metric NOUN ejpam-3086 6 34 manifold manifold ADJ ejpam-3086 6 35 1 1 NUM ejpam-3086 6 36 . . PUNCT ejpam-3086 7 1 introduction introduction NOUN ejpam-3086 7 2 j. j. PROPN ejpam-3086 7 3 eells eells PROPN ejpam-3086 7 4 and and CCONJ ejpam-3086 7 5 j. j. PROPN ejpam-3086 7 6 h. h. PROPN ejpam-3086 7 7 sampson sampson PROPN ejpam-3086 7 8 studied study VERB ejpam-3086 7 9 harmonic harmonic ADJ ejpam-3086 7 10 maps map NOUN ejpam-3086 7 11 on on ADP ejpam-3086 7 12 riemannian riemannian ADJ ejpam-3086 7 13 manifolds manifold NOUN ejpam-3086 7 14 ( ( PUNCT ejpam-3086 7 15 [ [ X ejpam-3086 7 16 8 8 NUM ejpam-3086 7 17 ] ] NUM ejpam-3086 7 18 ) ) PUNCT ejpam-3086 7 19 . . PUNCT ejpam-3086 8 1 also also ADV ejpam-3086 8 2 , , PUNCT ejpam-3086 8 3 they they PRON ejpam-3086 8 4 proved prove VERB ejpam-3086 8 5 that that SCONJ ejpam-3086 8 6 a a DET ejpam-3086 8 7 holomorphic holomorphic ADJ ejpam-3086 8 8 map map NOUN ejpam-3086 8 9 between between ADP ejpam-3086 8 10 kähler kähler PROPN ejpam-3086 8 11 manifolds manifold NOUN ejpam-3086 8 12 is be AUX ejpam-3086 8 13 a a DET ejpam-3086 8 14 harmonic harmonic ADJ ejpam-3086 8 15 map map NOUN ejpam-3086 8 16 . . PUNCT ejpam-3086 9 1 in in ADP ejpam-3086 9 2 odd odd ADJ ejpam-3086 9 3 dimension dimension NOUN ejpam-3086 9 4 , , PUNCT ejpam-3086 9 5 the the DET ejpam-3086 9 6 almost almost ADV ejpam-3086 9 7 contact contact NOUN ejpam-3086 9 8 metric metric ADJ ejpam-3086 9 9 manifolds manifold NOUN ejpam-3086 9 10 represent represent VERB ejpam-3086 9 11 the the DET ejpam-3086 9 12 analogue analogue NOUN ejpam-3086 9 13 of of ADP ejpam-3086 9 14 almost almost ADV ejpam-3086 9 15 hermitian hermitian ADJ ejpam-3086 9 16 manifolds manifold NOUN ejpam-3086 9 17 ( ( PUNCT ejpam-3086 9 18 see see VERB ejpam-3086 9 19 [ [ X ejpam-3086 9 20 2 2 NUM ejpam-3086 9 21 ] ] PUNCT ejpam-3086 9 22 , , PUNCT ejpam-3086 9 23 [ [ X ejpam-3086 9 24 3 3 NUM ejpam-3086 9 25 ] ] NUM ejpam-3086 9 26 ) ) PUNCT ejpam-3086 9 27 . . PUNCT ejpam-3086 10 1 s. s. PROPN ejpam-3086 10 2 ianus ianus PROPN ejpam-3086 10 3 and and CCONJ ejpam-3086 10 4 a. a. NOUN ejpam-3086 10 5 m. m. PROPN ejpam-3086 10 6 pastore pastore PROPN ejpam-3086 10 7 , , PUNCT ejpam-3086 10 8 considered consider VERB ejpam-3086 10 9 ( ( PUNCT ejpam-3086 10 10 φ φ NUM ejpam-3086 10 11 , , PUNCT ejpam-3086 10 12 φ́)-holomorphic φ́)-holomorphic ADJ ejpam-3086 10 13 maps map NOUN ejpam-3086 10 14 between between ADP ejpam-3086 10 15 contact contact NOUN ejpam-3086 10 16 metric metric ADJ ejpam-3086 10 17 ( ( PUNCT ejpam-3086 10 18 or or CCONJ ejpam-3086 10 19 sasakian sasakian ADJ ejpam-3086 10 20 ) ) PUNCT ejpam-3086 10 21 manifolds manifold NOUN ejpam-3086 10 22 and and CCONJ ejpam-3086 10 23 proved prove VERB ejpam-3086 10 24 that that SCONJ ejpam-3086 10 25 such such ADJ ejpam-3086 10 26 maps map NOUN ejpam-3086 10 27 are be AUX ejpam-3086 10 28 harmonic harmonic ADJ ejpam-3086 10 29 ( ( PUNCT ejpam-3086 10 30 [ [ X ejpam-3086 10 31 9 9 NUM ejpam-3086 10 32 ] ] NUM ejpam-3086 10 33 ) ) PUNCT ejpam-3086 10 34 . . PUNCT ejpam-3086 11 1 contact contact NOUN ejpam-3086 11 2 metric metric ADJ ejpam-3086 11 3 manifolds manifold NOUN ejpam-3086 11 4 are be AUX ejpam-3086 11 5 ( ( PUNCT ejpam-3086 11 6 φ φ PROPN ejpam-3086 11 7 , , PUNCT ejpam-3086 11 8 ξ ξ PROPN ejpam-3086 11 9 , , PUNCT ejpam-3086 11 10 η η NOUN ejpam-3086 11 11 , , PUNCT ejpam-3086 11 12 g)almost g)almost ADJ ejpam-3086 11 13 contact contact NOUN ejpam-3086 11 14 metric metric ADJ ejpam-3086 11 15 manifolds manifold NOUN ejpam-3086 11 16 in in ADP ejpam-3086 11 17 which which PRON ejpam-3086 11 18 dη dη X ejpam-3086 11 19 = = SYM ejpam-3086 11 20 φ φ PROPN ejpam-3086 11 21 . . PUNCT ejpam-3086 12 1 in in ADP ejpam-3086 12 2 this this DET ejpam-3086 12 3 paper paper NOUN ejpam-3086 12 4 , , PUNCT ejpam-3086 12 5 we we PRON ejpam-3086 12 6 study study VERB ejpam-3086 12 7 ( ( PUNCT ejpam-3086 12 8 φ φ PROPN ejpam-3086 12 9 , , PUNCT ejpam-3086 12 10 φ́)-holomorphic φ́)-holomorphic ADJ ejpam-3086 12 11 maps map NOUN ejpam-3086 12 12 between between ADP ejpam-3086 12 13 two two NUM ejpam-3086 12 14 classes class NOUN ejpam-3086 12 15 of of ADP ejpam-3086 12 16 almost almost ADV ejpam-3086 12 17 contact contact NOUN ejpam-3086 12 18 metric metric ADJ ejpam-3086 12 19 manifolds manifold NOUN ejpam-3086 12 20 in in ADP ejpam-3086 12 21 which which PRON ejpam-3086 12 22 dη+ dη+ NOUN ejpam-3086 12 23 dηoφ⊗φ dηoφ⊗φ VERB ejpam-3086 12 24 = = SYM ejpam-3086 12 25 2φ 2φ NUM ejpam-3086 12 26 . . PUNCT ejpam-3086 13 1 nearly nearly ADV ejpam-3086 13 2 sasakian sasakian ADJ ejpam-3086 13 3 and and CCONJ ejpam-3086 13 4 quasi quasi ADJ ejpam-3086 13 5 contact contact NOUN ejpam-3086 13 6 metric metric ADJ ejpam-3086 13 7 manifolds manifold NOUN ejpam-3086 13 8 are be AUX ejpam-3086 13 9 examples example NOUN ejpam-3086 13 10 of of ADP ejpam-3086 13 11 these these DET ejpam-3086 13 12 kind kind NOUN ejpam-3086 13 13 of of ADP ejpam-3086 13 14 manifolds manifold NOUN ejpam-3086 13 15 ( ( PUNCT ejpam-3086 13 16 contact contact NOUN ejpam-3086 13 17 metric metric ADJ ejpam-3086 13 18 manifolds manifold NOUN ejpam-3086 13 19 , , PUNCT ejpam-3086 13 20 satisfy satisfy VERB ejpam-3086 13 21 this this DET ejpam-3086 13 22 relation relation NOUN ejpam-3086 13 23 too too ADV ejpam-3086 13 24 , , PUNCT ejpam-3086 13 25 because because SCONJ ejpam-3086 13 26 in in ADP ejpam-3086 13 27 contact contact NOUN ejpam-3086 13 28 metric metric ADJ ejpam-3086 13 29 manifolds manifold NOUN ejpam-3086 13 30 we we PRON ejpam-3086 13 31 have have VERB ejpam-3086 13 32 dηoφ⊗φ dηoφ⊗φ NOUN ejpam-3086 13 33 = = PUNCT ejpam-3086 13 34 dη dη NOUN ejpam-3086 13 35 ) ) PUNCT ejpam-3086 13 36 . . PUNCT ejpam-3086 14 1 also also ADV ejpam-3086 14 2 , , PUNCT ejpam-3086 14 3 conformal conformal ADJ ejpam-3086 14 4 transformation transformation NOUN ejpam-3086 14 5 on on ADP ejpam-3086 14 6 these these DET ejpam-3086 14 7 manifolds manifold NOUN ejpam-3086 14 8 are be AUX ejpam-3086 14 9 considered consider VERB ejpam-3086 14 10 in in ADP ejpam-3086 14 11 this this DET ejpam-3086 14 12 paper paper NOUN ejpam-3086 14 13 . . PUNCT ejpam-3086 15 1 in in ADP ejpam-3086 15 2 [ [ X ejpam-3086 15 3 6 6 NUM ejpam-3086 15 4 ] ] PUNCT ejpam-3086 15 5 , , PUNCT ejpam-3086 15 6 tanno tanno PROPN ejpam-3086 15 7 studied study VERB ejpam-3086 15 8 conformal conformal ADJ ejpam-3086 15 9 transformation transformation NOUN ejpam-3086 15 10 on on ADP ejpam-3086 15 11 contact contact NOUN ejpam-3086 15 12 metric metric ADJ ejpam-3086 15 13 manifolds manifold NOUN ejpam-3086 15 14 . . PUNCT ejpam-3086 15 15 ∗corresponding ∗corresponde VERB ejpam-3086 15 16 author author NOUN ejpam-3086 15 17 . . PUNCT ejpam-3086 16 1 email email NOUN ejpam-3086 16 2 addresses address NOUN ejpam-3086 16 3 : : PUNCT ejpam-3086 16 4 malek@kntu.ac.ir malek@kntu.ac.ir PROPN ejpam-3086 16 5 ( ( PUNCT ejpam-3086 16 6 f. f. PROPN ejpam-3086 16 7 malek malek PROPN ejpam-3086 16 8 ) ) PUNCT ejpam-3086 16 9 , , PUNCT ejpam-3086 16 10 samani108@yahoo.com samani108@yahoo.com X ejpam-3086 16 11 ( ( PUNCT ejpam-3086 16 12 m. m. NOUN ejpam-3086 16 13 samanipour samanipour PROPN ejpam-3086 16 14 ) ) PUNCT ejpam-3086 16 15 http://www.ejpam.com http://www.ejpam.com X ejpam-3086 17 1 946 946 NUM ejpam-3086 17 2 c c X ejpam-3086 17 3 © © PROPN ejpam-3086 17 4 2017 2017 NUM ejpam-3086 17 5 ejpam ejpam VERB ejpam-3086 17 6 all all DET ejpam-3086 17 7 rights right NOUN ejpam-3086 17 8 reserved reserve VERB ejpam-3086 17 9 . . PUNCT ejpam-3086 18 1 f. f. PROPN ejpam-3086 18 2 malek malek PROPN ejpam-3086 18 3 , , PUNCT ejpam-3086 18 4 m. m. NOUN ejpam-3086 18 5 samanipour samanipour PROPN ejpam-3086 18 6 / / SYM ejpam-3086 18 7 eur eur PROPN ejpam-3086 18 8 . . PUNCT ejpam-3086 19 1 j. j. PROPN ejpam-3086 19 2 pure pure PROPN ejpam-3086 19 3 appl appl PROPN ejpam-3086 19 4 . . PROPN ejpam-3086 19 5 math math PROPN ejpam-3086 19 6 , , PUNCT ejpam-3086 19 7 10 10 NUM ejpam-3086 19 8 ( ( PUNCT ejpam-3086 19 9 5 5 NUM ejpam-3086 19 10 ) ) PUNCT ejpam-3086 19 11 ( ( PUNCT ejpam-3086 19 12 2017 2017 NUM ejpam-3086 19 13 ) ) PUNCT ejpam-3086 19 14 , , PUNCT ejpam-3086 19 15 946 946 NUM ejpam-3086 19 16 - - SYM ejpam-3086 19 17 954 954 NUM ejpam-3086 19 18 947 947 NUM ejpam-3086 19 19 2 2 NUM ejpam-3086 19 20 . . PUNCT ejpam-3086 19 21 preliminaries preliminary NOUN ejpam-3086 19 22 a a DET ejpam-3086 19 23 contact contact NOUN ejpam-3086 19 24 manifold manifold NOUN ejpam-3086 19 25 is be AUX ejpam-3086 19 26 a a DET ejpam-3086 19 27 c∞ c∞ PROPN ejpam-3086 19 28 manifold manifold ADJ ejpam-3086 19 29 m2n+1 m2n+1 NOUN ejpam-3086 19 30 together together ADV ejpam-3086 19 31 with with ADP ejpam-3086 19 32 a a DET ejpam-3086 19 33 1 1 NUM ejpam-3086 19 34 - - PUNCT ejpam-3086 19 35 form form NOUN ejpam-3086 19 36 η η NOUN ejpam-3086 19 37 such such ADJ ejpam-3086 19 38 that that SCONJ ejpam-3086 19 39 η η PROPN ejpam-3086 19 40 ∧ ∧ PROPN ejpam-3086 19 41 ( ( PUNCT ejpam-3086 19 42 dη)n dη)n PROPN ejpam-3086 19 43 6= 6= PRON ejpam-3086 19 44 0 0 NUM ejpam-3086 19 45 . . PUNCT ejpam-3086 20 1 in in ADP ejpam-3086 20 2 a a DET ejpam-3086 20 3 contact contact NOUN ejpam-3086 20 4 manifold manifold ADJ ejpam-3086 20 5 ( ( PUNCT ejpam-3086 20 6 m m PROPN ejpam-3086 20 7 , , PUNCT ejpam-3086 20 8 η η NOUN ejpam-3086 20 9 ) ) PUNCT ejpam-3086 20 10 we we PRON ejpam-3086 20 11 can can AUX ejpam-3086 20 12 choose choose VERB ejpam-3086 20 13 a a DET ejpam-3086 20 14 vector vector NOUN ejpam-3086 20 15 field field NOUN ejpam-3086 20 16 ξ ξ NOUN ejpam-3086 20 17 , , PUNCT ejpam-3086 20 18 called call VERB ejpam-3086 20 19 characteristic characteristic ADJ ejpam-3086 20 20 vector vector NOUN ejpam-3086 20 21 field field NOUN ejpam-3086 20 22 , , PUNCT ejpam-3086 20 23 such such ADJ ejpam-3086 20 24 that that SCONJ ejpam-3086 20 25 dη(ξ dη(ξ ADJ ejpam-3086 20 26 , , PUNCT ejpam-3086 20 27 x x X ejpam-3086 20 28 ) ) PUNCT ejpam-3086 20 29 = = SYM ejpam-3086 20 30 0 0 NUM ejpam-3086 20 31 and and CCONJ ejpam-3086 20 32 η(ξ η(ξ PROPN ejpam-3086 20 33 ) ) PUNCT ejpam-3086 20 34 = = SYM ejpam-3086 21 1 1 1 X ejpam-3086 21 2 . . X ejpam-3086 22 1 we we PRON ejpam-3086 22 2 say say VERB ejpam-3086 22 3 that that SCONJ ejpam-3086 22 4 a a DET ejpam-3086 22 5 riemannian riemannian ADJ ejpam-3086 22 6 manifold manifold NOUN ejpam-3086 22 7 ( ( PUNCT ejpam-3086 22 8 m m PROPN ejpam-3086 22 9 , , PUNCT ejpam-3086 22 10 g g NOUN ejpam-3086 22 11 ) ) PUNCT ejpam-3086 22 12 has have VERB ejpam-3086 22 13 an an DET ejpam-3086 22 14 almost almost ADV ejpam-3086 22 15 contact contact NOUN ejpam-3086 22 16 metric metric ADJ ejpam-3086 22 17 structure structure NOUN ejpam-3086 22 18 , , PUNCT ejpam-3086 22 19 if if SCONJ ejpam-3086 22 20 it it PRON ejpam-3086 22 21 admits admit VERB ejpam-3086 22 22 a a DET ejpam-3086 22 23 tensor tensor NOUN ejpam-3086 22 24 field field NOUN ejpam-3086 22 25 φ φ PROPN ejpam-3086 22 26 of of ADP ejpam-3086 22 27 type type NOUN ejpam-3086 22 28 ( ( PUNCT ejpam-3086 22 29 1,1 1,1 NUM ejpam-3086 22 30 ) ) PUNCT ejpam-3086 22 31 , , PUNCT ejpam-3086 22 32 a a DET ejpam-3086 22 33 vector vector NOUN ejpam-3086 22 34 field field NOUN ejpam-3086 22 35 ξ ξ PROPN ejpam-3086 22 36 and and CCONJ ejpam-3086 22 37 a a DET ejpam-3086 22 38 1 1 NUM ejpam-3086 22 39 - - PUNCT ejpam-3086 22 40 form form NOUN ejpam-3086 22 41 η η NOUN ejpam-3086 22 42 satisfying satisfy VERB ejpam-3086 22 43 the the DET ejpam-3086 22 44 following follow VERB ejpam-3086 22 45 relations relation NOUN ejpam-3086 22 46 φ2 φ2 PROPN ejpam-3086 22 47 = = SYM ejpam-3086 23 1 −i −i PROPN ejpam-3086 23 2 + + CCONJ ejpam-3086 23 3 η η PROPN ejpam-3086 23 4 ⊗ ⊗ PROPN ejpam-3086 23 5 ξ ξ PROPN ejpam-3086 23 6 , , PUNCT ejpam-3086 23 7 g(x g(x PROPN ejpam-3086 23 8 , , PUNCT ejpam-3086 23 9 ξ ξ NOUN ejpam-3086 23 10 ) ) PUNCT ejpam-3086 23 11 = = SYM ejpam-3086 23 12 η(x η(x NOUN ejpam-3086 23 13 ) ) PUNCT ejpam-3086 23 14 , , PUNCT ejpam-3086 23 15 g(φx g(φx NOUN ejpam-3086 23 16 , , PUNCT ejpam-3086 23 17 φy φy NOUN ejpam-3086 23 18 ) ) PUNCT ejpam-3086 24 1 = = SYM ejpam-3086 24 2 g(x g(x NOUN ejpam-3086 24 3 , , PUNCT ejpam-3086 24 4 y y PROPN ejpam-3086 24 5 ) ) PUNCT ejpam-3086 24 6 − − PROPN ejpam-3086 24 7 η(x)η(y η(x)η(y NOUN ejpam-3086 24 8 ) ) PUNCT ejpam-3086 24 9 . . PUNCT ejpam-3086 25 1 it it PRON ejpam-3086 25 2 is be AUX ejpam-3086 25 3 proved prove VERB ejpam-3086 25 4 that that SCONJ ejpam-3086 25 5 given give VERB ejpam-3086 25 6 a a DET ejpam-3086 25 7 contact contact NOUN ejpam-3086 25 8 manifold manifold ADJ ejpam-3086 25 9 ( ( PUNCT ejpam-3086 25 10 m m PROPN ejpam-3086 25 11 , , PUNCT ejpam-3086 25 12 η η NOUN ejpam-3086 25 13 ) ) PUNCT ejpam-3086 25 14 with with ADP ejpam-3086 25 15 characteristic characteristic ADJ ejpam-3086 25 16 vector vector NOUN ejpam-3086 25 17 field field NOUN ejpam-3086 25 18 ξ ξ PROPN ejpam-3086 25 19 , , PUNCT ejpam-3086 25 20 there there PRON ejpam-3086 25 21 exists exist VERB ejpam-3086 25 22 an an DET ejpam-3086 25 23 almost almost ADV ejpam-3086 25 24 contact contact NOUN ejpam-3086 25 25 metric metric ADJ ejpam-3086 25 26 structure(φ structure(φ NOUN ejpam-3086 25 27 , , PUNCT ejpam-3086 25 28 ξ ξ PROPN ejpam-3086 25 29 , , PUNCT ejpam-3086 25 30 η η NOUN ejpam-3086 25 31 , , PUNCT ejpam-3086 25 32 g g NOUN ejpam-3086 25 33 ) ) PUNCT ejpam-3086 25 34 such such ADJ ejpam-3086 25 35 that that SCONJ ejpam-3086 25 36 dη(x dη(x PROPN ejpam-3086 25 37 , , PUNCT ejpam-3086 25 38 y y PROPN ejpam-3086 25 39 ) ) PUNCT ejpam-3086 25 40 = = SYM ejpam-3086 26 1 φ(x φ(x PROPN ejpam-3086 26 2 , , PUNCT ejpam-3086 26 3 y y PROPN ejpam-3086 26 4 ) ) PUNCT ejpam-3086 26 5 , , PUNCT ejpam-3086 26 6 in in ADP ejpam-3086 26 7 which which PRON ejpam-3086 26 8 φ(x φ(x PROPN ejpam-3086 26 9 , , PUNCT ejpam-3086 26 10 y y NOUN ejpam-3086 26 11 ) ) PUNCT ejpam-3086 26 12 = = PUNCT ejpam-3086 27 1 g(x g(x NOUN ejpam-3086 27 2 , , PUNCT ejpam-3086 27 3 φy φy NOUN ejpam-3086 27 4 ) ) PUNCT ejpam-3086 27 5 . . PUNCT ejpam-3086 28 1 in in ADP ejpam-3086 28 2 this this DET ejpam-3086 28 3 case case NOUN ejpam-3086 28 4 , , PUNCT ejpam-3086 28 5 we we PRON ejpam-3086 28 6 say say VERB ejpam-3086 28 7 that that SCONJ ejpam-3086 28 8 m m NOUN ejpam-3086 28 9 is be AUX ejpam-3086 28 10 equipped equip VERB ejpam-3086 28 11 with with ADP ejpam-3086 28 12 a a DET ejpam-3086 28 13 ( ( PUNCT ejpam-3086 28 14 φ φ PROPN ejpam-3086 28 15 , , PUNCT ejpam-3086 28 16 ξ ξ PROPN ejpam-3086 28 17 , , PUNCT ejpam-3086 28 18 η η NOUN ejpam-3086 28 19 , , PUNCT ejpam-3086 28 20 g g NOUN ejpam-3086 28 21 ) ) PUNCT ejpam-3086 28 22 contact contact NOUN ejpam-3086 28 23 metric metric ADJ ejpam-3086 28 24 structure structure NOUN ejpam-3086 28 25 . . PUNCT ejpam-3086 29 1 we we PRON ejpam-3086 29 2 mention mention VERB ejpam-3086 29 3 that that SCONJ ejpam-3086 29 4 it it PRON ejpam-3086 29 5 is be AUX ejpam-3086 29 6 possible possible ADJ ejpam-3086 29 7 to to PART ejpam-3086 29 8 have have VERB ejpam-3086 29 9 a a DET ejpam-3086 29 10 contact contact NOUN ejpam-3086 29 11 manifold manifold NOUN ejpam-3086 29 12 m m NOUN ejpam-3086 29 13 = = SYM ejpam-3086 29 14 ( ( PUNCT ejpam-3086 29 15 m m PROPN ejpam-3086 29 16 , , PUNCT ejpam-3086 29 17 η η NOUN ejpam-3086 29 18 ) ) PUNCT ejpam-3086 29 19 with with ADP ejpam-3086 29 20 characteristic characteristic ADJ ejpam-3086 29 21 vector vector NOUN ejpam-3086 29 22 field field NOUN ejpam-3086 29 23 ξ ξ PROPN ejpam-3086 29 24 and and CCONJ ejpam-3086 29 25 with with ADP ejpam-3086 29 26 ( ( PUNCT ejpam-3086 29 27 φ φ PROPN ejpam-3086 29 28 , , PUNCT ejpam-3086 29 29 ξ ξ PROPN ejpam-3086 29 30 , , PUNCT ejpam-3086 29 31 η η NOUN ejpam-3086 29 32 , , PUNCT ejpam-3086 29 33 g)-almost g)-almost PUNCT ejpam-3086 29 34 contact contact NOUN ejpam-3086 29 35 metric metric ADJ ejpam-3086 29 36 structure structure NOUN ejpam-3086 29 37 , , PUNCT ejpam-3086 29 38 same same ADJ ejpam-3086 29 39 ξ ξ PROPN ejpam-3086 29 40 and and CCONJ ejpam-3086 29 41 η η PROPN ejpam-3086 29 42 , , PUNCT ejpam-3086 29 43 in in ADP ejpam-3086 29 44 which which PRON ejpam-3086 29 45 dη(x dη(x PROPN ejpam-3086 29 46 , , PUNCT ejpam-3086 29 47 y y PROPN ejpam-3086 29 48 ) ) PUNCT ejpam-3086 29 49 6= 6= ADP ejpam-3086 30 1 g(x g(x NOUN ejpam-3086 30 2 , , PUNCT ejpam-3086 30 3 φy φy NOUN ejpam-3086 30 4 ) ) PUNCT ejpam-3086 30 5 , , PUNCT ejpam-3086 30 6 then then ADV ejpam-3086 30 7 m m VERB ejpam-3086 30 8 = = SYM ejpam-3086 30 9 ( ( PUNCT ejpam-3086 30 10 m m PROPN ejpam-3086 30 11 , , PUNCT ejpam-3086 30 12 φ φ PROPN ejpam-3086 30 13 , , PUNCT ejpam-3086 30 14 ξ ξ PROPN ejpam-3086 30 15 , , PUNCT ejpam-3086 30 16 η η NOUN ejpam-3086 30 17 , , PUNCT ejpam-3086 30 18 g g NOUN ejpam-3086 30 19 ) ) PUNCT ejpam-3086 30 20 is be AUX ejpam-3086 30 21 contact contact NOUN ejpam-3086 30 22 but but CCONJ ejpam-3086 30 23 not not PART ejpam-3086 30 24 contact contact NOUN ejpam-3086 30 25 metric metric NOUN ejpam-3086 30 26 . . PUNCT ejpam-3086 31 1 y. y. PROPN ejpam-3086 31 2 tashiro tashiro PROPN ejpam-3086 31 3 studied study VERB ejpam-3086 31 4 almost almost ADV ejpam-3086 31 5 contact contact NOUN ejpam-3086 31 6 manifolds manifold NOUN ejpam-3086 31 7 as as ADP ejpam-3086 31 8 hypersurfaces hypersurface NOUN ejpam-3086 31 9 of of ADP ejpam-3086 31 10 almost almost ADV ejpam-3086 31 11 complex complex ADJ ejpam-3086 31 12 manifolds manifold NOUN ejpam-3086 31 13 ( ( PUNCT ejpam-3086 31 14 [ [ X ejpam-3086 31 15 16 16 NUM ejpam-3086 31 16 ] ] PUNCT ejpam-3086 31 17 ) ) PUNCT ejpam-3086 31 18 . . PUNCT ejpam-3086 32 1 he he PRON ejpam-3086 32 2 showed show VERB ejpam-3086 32 3 that that SCONJ ejpam-3086 32 4 a a DET ejpam-3086 32 5 hypersurface hypersurface NOUN ejpam-3086 32 6 in in ADP ejpam-3086 32 7 an an DET ejpam-3086 32 8 almost almost ADV ejpam-3086 32 9 hermitian hermitian ADJ ejpam-3086 32 10 manifold manifold PROPN ejpam-3086 32 11 has have VERB ejpam-3086 32 12 an an DET ejpam-3086 32 13 almost almost ADV ejpam-3086 32 14 contact contact NOUN ejpam-3086 32 15 metric metric ADJ ejpam-3086 32 16 structure structure NOUN ejpam-3086 32 17 and and CCONJ ejpam-3086 32 18 when when SCONJ ejpam-3086 32 19 the the DET ejpam-3086 32 20 almost almost ADV ejpam-3086 32 21 hermitian hermitian ADJ ejpam-3086 32 22 manifold manifold NOUN ejpam-3086 32 23 is be AUX ejpam-3086 32 24 quasi quasi ADJ ejpam-3086 32 25 kähler kähler NOUN ejpam-3086 32 26 , , PUNCT ejpam-3086 32 27 he he PRON ejpam-3086 32 28 called call VERB ejpam-3086 32 29 it it PRON ejpam-3086 32 30 ’s ’s AUX ejpam-3086 32 31 associated associate VERB ejpam-3086 32 32 almost almost ADV ejpam-3086 32 33 contact contact NOUN ejpam-3086 32 34 metric metric ADJ ejpam-3086 32 35 hypersurface hypersurface NOUN ejpam-3086 32 36 , , PUNCT ejpam-3086 32 37 contact contact NOUN ejpam-3086 32 38 o∗−manifold o∗−manifold PROPN ejpam-3086 32 39 . . PUNCT ejpam-3086 33 1 then then ADV ejpam-3086 33 2 j. j. PROPN ejpam-3086 33 3 h. h. PROPN ejpam-3086 33 4 kim kim PROPN ejpam-3086 33 5 , , PUNCT ejpam-3086 33 6 j. j. PROPN ejpam-3086 33 7 h. h. PROPN ejpam-3086 33 8 park park PROPN ejpam-3086 33 9 and and CCONJ ejpam-3086 33 10 k. k. PROPN ejpam-3086 33 11 sekigawa sekigawa PROPN ejpam-3086 33 12 called call VERB ejpam-3086 33 13 such such DET ejpam-3086 33 14 an an DET ejpam-3086 33 15 almost almost ADV ejpam-3086 33 16 contact contact NOUN ejpam-3086 33 17 metric metric NOUN ejpam-3086 33 18 manifold manifold ADJ ejpam-3086 33 19 a a DET ejpam-3086 33 20 quasi quasi ADJ ejpam-3086 33 21 contact contact NOUN ejpam-3086 33 22 metric metric NOUN ejpam-3086 33 23 manifold manifold NOUN ejpam-3086 33 24 ( ( PUNCT ejpam-3086 33 25 [ [ X ejpam-3086 33 26 10 10 NUM ejpam-3086 33 27 ] ] NUM ejpam-3086 33 28 ) ) PUNCT ejpam-3086 33 29 . . PUNCT ejpam-3086 34 1 they they PRON ejpam-3086 34 2 proved prove VERB ejpam-3086 34 3 that that SCONJ ejpam-3086 34 4 an an DET ejpam-3086 34 5 almost almost ADV ejpam-3086 34 6 contact contact NOUN ejpam-3086 34 7 metric metric ADJ ejpam-3086 34 8 manifold manifold ADJ ejpam-3086 34 9 m m NOUN ejpam-3086 34 10 = = SYM ejpam-3086 34 11 ( ( PUNCT ejpam-3086 34 12 m m PROPN ejpam-3086 34 13 , , PUNCT ejpam-3086 34 14 φ φ PROPN ejpam-3086 34 15 , , PUNCT ejpam-3086 34 16 ξ ξ PROPN ejpam-3086 34 17 , , PUNCT ejpam-3086 34 18 η η NOUN ejpam-3086 34 19 , , PUNCT ejpam-3086 34 20 g g NOUN ejpam-3086 34 21 ) ) PUNCT ejpam-3086 34 22 is be AUX ejpam-3086 34 23 quasi quasi ADJ ejpam-3086 34 24 contact contact NOUN ejpam-3086 34 25 metric metric ADJ ejpam-3086 35 1 if if SCONJ ejpam-3086 35 2 and and CCONJ ejpam-3086 35 3 only only ADV ejpam-3086 35 4 if if SCONJ ejpam-3086 35 5 it it PRON ejpam-3086 35 6 satisfies satisfy VERB ejpam-3086 35 7 the the DET ejpam-3086 35 8 following follow VERB ejpam-3086 35 9 relation relation NOUN ejpam-3086 35 10 : : PUNCT ejpam-3086 35 11 ( ( PUNCT ejpam-3086 35 12 ∇xφ)y ∇xφ)y NOUN ejpam-3086 35 13 + + X ejpam-3086 35 14 ( ( PUNCT ejpam-3086 35 15 ∇φxφ)φy ∇φxφ)φy NOUN ejpam-3086 35 16 = = SYM ejpam-3086 35 17 2g(x 2g(x NUM ejpam-3086 35 18 , , PUNCT ejpam-3086 35 19 y y PROPN ejpam-3086 35 20 ) ) PUNCT ejpam-3086 35 21 ξ ξ PROPN ejpam-3086 35 22 − − PROPN ejpam-3086 35 23 η(y η(y PROPN ejpam-3086 35 24 ) ) PUNCT ejpam-3086 35 25 ( ( PUNCT ejpam-3086 35 26 x x X ejpam-3086 36 1 + + CCONJ ejpam-3086 36 2 η(x)ξ η(x)ξ PROPN ejpam-3086 36 3 + + NUM ejpam-3086 36 4 hx hx PROPN ejpam-3086 36 5 ) ) PUNCT ejpam-3086 36 6 , , PUNCT ejpam-3086 36 7 ( ( PUNCT ejpam-3086 36 8 1 1 X ejpam-3086 36 9 ) ) PUNCT ejpam-3086 36 10 for for ADP ejpam-3086 36 11 every every DET ejpam-3086 36 12 vector vector NOUN ejpam-3086 36 13 fields field NOUN ejpam-3086 36 14 x x PUNCT ejpam-3086 36 15 and and CCONJ ejpam-3086 36 16 y y PROPN ejpam-3086 36 17 on on ADP ejpam-3086 36 18 m m PROPN ejpam-3086 36 19 , , PUNCT ejpam-3086 36 20 in in ADP ejpam-3086 36 21 which which PRON ejpam-3086 36 22 h h NOUN ejpam-3086 36 23 : : PUNCT ejpam-3086 36 24 = = SYM ejpam-3086 36 25 1 1 NUM ejpam-3086 36 26 2lξφ 2lξφ NOUN ejpam-3086 36 27 . . PUNCT ejpam-3086 37 1 the the DET ejpam-3086 37 2 above above ADJ ejpam-3086 37 3 relation relation NOUN ejpam-3086 37 4 holds hold VERB ejpam-3086 37 5 in in ADP ejpam-3086 37 6 every every DET ejpam-3086 37 7 contact contact NOUN ejpam-3086 37 8 metric metric NOUN ejpam-3086 37 9 manifold manifold NOUN ejpam-3086 37 10 ( ( PUNCT ejpam-3086 37 11 [ [ X ejpam-3086 37 12 3 3 NUM ejpam-3086 37 13 ] ] PUNCT ejpam-3086 37 14 , , PUNCT ejpam-3086 37 15 page116 page116 PROPN ejpam-3086 37 16 ) ) PUNCT ejpam-3086 37 17 , , PUNCT ejpam-3086 37 18 thus thus ADV ejpam-3086 37 19 quasi quasi ADJ ejpam-3086 37 20 contact contact NOUN ejpam-3086 37 21 metric metric ADJ ejpam-3086 37 22 manifolds manifold NOUN ejpam-3086 37 23 can can AUX ejpam-3086 37 24 be be AUX ejpam-3086 37 25 regarded regard VERB ejpam-3086 37 26 as as ADP ejpam-3086 37 27 a a DET ejpam-3086 37 28 generalization generalization NOUN ejpam-3086 37 29 of of ADP ejpam-3086 37 30 contact contact NOUN ejpam-3086 37 31 metric metric ADJ ejpam-3086 37 32 manifolds manifold NOUN ejpam-3086 37 33 . . PUNCT ejpam-3086 38 1 an an DET ejpam-3086 38 2 almost almost ADV ejpam-3086 38 3 contact contact NOUN ejpam-3086 38 4 metric metric ADJ ejpam-3086 38 5 structure structure NOUN ejpam-3086 38 6 ( ( PUNCT ejpam-3086 38 7 φ φ PROPN ejpam-3086 38 8 , , PUNCT ejpam-3086 38 9 ξ ξ PROPN ejpam-3086 38 10 , , PUNCT ejpam-3086 38 11 η η NOUN ejpam-3086 38 12 , , PUNCT ejpam-3086 38 13 g g NOUN ejpam-3086 38 14 ) ) PUNCT ejpam-3086 38 15 is be AUX ejpam-3086 38 16 said say VERB ejpam-3086 38 17 to to PART ejpam-3086 38 18 be be AUX ejpam-3086 38 19 nearly nearly ADV ejpam-3086 38 20 sasakian sasakian ADJ ejpam-3086 38 21 iff iff PROPN ejpam-3086 38 22 ( ( PUNCT ejpam-3086 38 23 ∇xφ)y ∇xφ)y PROPN ejpam-3086 38 24 + + CCONJ ejpam-3086 38 25 ( ( PUNCT ejpam-3086 38 26 ∇y ∇y PROPN ejpam-3086 38 27 φ)x φ)x ADJ ejpam-3086 38 28 = = SYM ejpam-3086 38 29 2g(x 2g(x NUM ejpam-3086 38 30 , , PUNCT ejpam-3086 38 31 y y PROPN ejpam-3086 39 1 ) ) PUNCT ejpam-3086 39 2 ξ ξ X ejpam-3086 39 3 − − PUNCT ejpam-3086 39 4 η(x)y η(x)y PROPN ejpam-3086 39 5 − − PROPN ejpam-3086 39 6 η(y η(y NOUN ejpam-3086 39 7 ) ) PUNCT ejpam-3086 39 8 x x X ejpam-3086 39 9 ( ( PUNCT ejpam-3086 39 10 2 2 NUM ejpam-3086 39 11 ) ) PUNCT ejpam-3086 39 12 for for ADP ejpam-3086 39 13 every every DET ejpam-3086 39 14 vector vector NOUN ejpam-3086 39 15 fields field NOUN ejpam-3086 39 16 x x X ejpam-3086 39 17 , , PUNCT ejpam-3086 39 18 y y PROPN ejpam-3086 39 19 on on ADP ejpam-3086 39 20 m m PROPN ejpam-3086 39 21 . . PUNCT ejpam-3086 40 1 nearly nearly ADV ejpam-3086 40 2 sasakian sasakian ADJ ejpam-3086 40 3 manifolds manifold NOUN ejpam-3086 40 4 were be AUX ejpam-3086 40 5 introduced introduce VERB ejpam-3086 40 6 in in ADP ejpam-3086 40 7 1976 1976 NUM ejpam-3086 40 8 by by ADP ejpam-3086 40 9 blair blair PROPN ejpam-3086 40 10 and and CCONJ ejpam-3086 40 11 his his PRON ejpam-3086 40 12 collaborators[4 collaborators[4 NOUN ejpam-3086 40 13 ] ] PUNCT ejpam-3086 40 14 . . PUNCT ejpam-3086 41 1 they they PRON ejpam-3086 41 2 proved prove VERB ejpam-3086 41 3 that that SCONJ ejpam-3086 41 4 every every DET ejpam-3086 41 5 sasakian sasakian NOUN ejpam-3086 41 6 manifold manifold NOUN ejpam-3086 41 7 is be AUX ejpam-3086 41 8 nearly nearly ADV ejpam-3086 41 9 sasakian sasakian ADJ ejpam-3086 41 10 , , PUNCT ejpam-3086 41 11 but but CCONJ ejpam-3086 41 12 the the DET ejpam-3086 41 13 converse converse NOUN ejpam-3086 41 14 statement statement NOUN ejpam-3086 41 15 fails fail VERB ejpam-3086 41 16 in in ADP ejpam-3086 41 17 general general ADJ ejpam-3086 41 18 . . PUNCT ejpam-3086 42 1 in in ADP ejpam-3086 42 2 addition addition NOUN ejpam-3086 42 3 they they PRON ejpam-3086 42 4 proved prove VERB ejpam-3086 42 5 that that SCONJ ejpam-3086 42 6 a a DET ejpam-3086 42 7 normal normal ADJ ejpam-3086 42 8 nearly nearly ADV ejpam-3086 42 9 sasakian sasakian ADJ ejpam-3086 42 10 structure structure NOUN ejpam-3086 42 11 is be AUX ejpam-3086 42 12 sasakian sasakian ADJ ejpam-3086 42 13 . . PUNCT ejpam-3086 43 1 they they PRON ejpam-3086 43 2 also also ADV ejpam-3086 43 3 showed show VERB ejpam-3086 43 4 that that SCONJ ejpam-3086 43 5 a a DET ejpam-3086 43 6 hypersurface hypersurface NOUN ejpam-3086 43 7 of of ADP ejpam-3086 43 8 a a DET ejpam-3086 43 9 nearly nearly ADV ejpam-3086 43 10 kähler kähler NOUN ejpam-3086 43 11 manifold manifold ADJ ejpam-3086 43 12 is be AUX ejpam-3086 43 13 nearly nearly ADV ejpam-3086 43 14 sasakian sasakian ADJ ejpam-3086 43 15 if if SCONJ ejpam-3086 44 1 and and CCONJ ejpam-3086 44 2 only only ADV ejpam-3086 44 3 if if SCONJ ejpam-3086 44 4 it it PRON ejpam-3086 44 5 is be AUX ejpam-3086 44 6 quasi quasi ADJ ejpam-3086 44 7 - - ADJ ejpam-3086 44 8 umbilical umbilical ADJ ejpam-3086 44 9 with with ADP ejpam-3086 44 10 respect respect NOUN ejpam-3086 44 11 to to ADP ejpam-3086 44 12 the the DET ejpam-3086 44 13 almost almost ADJ ejpam-3086 44 14 contact contact NOUN ejpam-3086 44 15 form form NOUN ejpam-3086 44 16 . . PUNCT ejpam-3086 45 1 in in ADP ejpam-3086 45 2 [ [ X ejpam-3086 45 3 5 5 NUM ejpam-3086 45 4 ] ] PUNCT ejpam-3086 45 5 f. f. PROPN ejpam-3086 45 6 malek malek PROPN ejpam-3086 45 7 , , PUNCT ejpam-3086 45 8 m. m. NOUN ejpam-3086 45 9 samanipour samanipour PROPN ejpam-3086 45 10 / / SYM ejpam-3086 45 11 eur eur PROPN ejpam-3086 45 12 . . PUNCT ejpam-3086 46 1 j. j. PROPN ejpam-3086 46 2 pure pure PROPN ejpam-3086 46 3 appl appl PROPN ejpam-3086 46 4 . . PROPN ejpam-3086 46 5 math math PROPN ejpam-3086 46 6 , , PUNCT ejpam-3086 46 7 10 10 NUM ejpam-3086 46 8 ( ( PUNCT ejpam-3086 46 9 5 5 NUM ejpam-3086 46 10 ) ) PUNCT ejpam-3086 46 11 ( ( PUNCT ejpam-3086 46 12 2017 2017 NUM ejpam-3086 46 13 ) ) PUNCT ejpam-3086 46 14 , , PUNCT ejpam-3086 46 15 946 946 NUM ejpam-3086 46 16 - - SYM ejpam-3086 46 17 954 954 NUM ejpam-3086 46 18 948 948 NUM ejpam-3086 46 19 it it PRON ejpam-3086 46 20 is be AUX ejpam-3086 46 21 proved prove VERB ejpam-3086 46 22 that that SCONJ ejpam-3086 46 23 nearly nearly ADV ejpam-3086 46 24 sasakian sasakian ADJ ejpam-3086 46 25 manifolds manifold NOUN ejpam-3086 46 26 are be AUX ejpam-3086 46 27 contact contact NOUN ejpam-3086 46 28 . . PUNCT ejpam-3086 47 1 in in ADP ejpam-3086 47 2 [ [ X ejpam-3086 47 3 1 1 NUM ejpam-3086 47 4 ] ] PUNCT ejpam-3086 47 5 , , PUNCT ejpam-3086 47 6 [ [ X ejpam-3086 47 7 4 4 NUM ejpam-3086 47 8 ] ] PUNCT ejpam-3086 47 9 , , PUNCT ejpam-3086 47 10 [ [ X ejpam-3086 47 11 7 7 NUM ejpam-3086 47 12 ] ] PUNCT ejpam-3086 47 13 , , PUNCT ejpam-3086 47 14 [ [ X ejpam-3086 47 15 11 11 NUM ejpam-3086 47 16 ] ] PUNCT ejpam-3086 47 17 , , PUNCT ejpam-3086 47 18 [ [ X ejpam-3086 47 19 12 12 NUM ejpam-3086 47 20 ] ] PUNCT ejpam-3086 47 21 , , PUNCT ejpam-3086 47 22 [ [ X ejpam-3086 47 23 13 13 NUM ejpam-3086 47 24 ] ] PUNCT ejpam-3086 47 25 and and CCONJ ejpam-3086 47 26 [ [ X ejpam-3086 47 27 15 15 NUM ejpam-3086 47 28 ] ] X ejpam-3086 47 29 , , PUNCT ejpam-3086 47 30 some some DET ejpam-3086 47 31 other other ADJ ejpam-3086 47 32 authors author NOUN ejpam-3086 47 33 studied study VERB ejpam-3086 47 34 nearly nearly ADV ejpam-3086 47 35 sasakian sasakian ADJ ejpam-3086 47 36 manifolds manifold NOUN ejpam-3086 47 37 . . PUNCT ejpam-3086 48 1 in in ADP ejpam-3086 48 2 this this DET ejpam-3086 48 3 paper paper NOUN ejpam-3086 48 4 , , PUNCT ejpam-3086 48 5 we we PRON ejpam-3086 48 6 study study VERB ejpam-3086 48 7 ( ( PUNCT ejpam-3086 48 8 φ φ PROPN ejpam-3086 48 9 , , PUNCT ejpam-3086 48 10 φ́)-holomorphic φ́)-holomorphic ADJ ejpam-3086 48 11 maps map NOUN ejpam-3086 48 12 between between ADP ejpam-3086 48 13 two two NUM ejpam-3086 48 14 quasi quasi ADJ ejpam-3086 48 15 contact contact NOUN ejpam-3086 48 16 metric metric NOUN ejpam-3086 48 17 ( ( PUNCT ejpam-3086 48 18 or or CCONJ ejpam-3086 48 19 nearly nearly ADV ejpam-3086 48 20 sasakain sasakain NOUN ejpam-3086 48 21 ) ) PUNCT ejpam-3086 48 22 manifolds manifold NOUN ejpam-3086 48 23 . . PUNCT ejpam-3086 49 1 they they PRON ejpam-3086 49 2 are be AUX ejpam-3086 49 3 two two NUM ejpam-3086 49 4 classes class NOUN ejpam-3086 49 5 of of ADP ejpam-3086 49 6 almost almost ADV ejpam-3086 49 7 contact contact NOUN ejpam-3086 49 8 metric metric ADJ ejpam-3086 49 9 manifolds manifold NOUN ejpam-3086 49 10 in in ADP ejpam-3086 49 11 which which PRON ejpam-3086 49 12 dη dη NOUN ejpam-3086 49 13 + + CCONJ ejpam-3086 49 14 dηoφ⊗ dηoφ⊗ PROPN ejpam-3086 49 15 φ φ PROPN ejpam-3086 49 16 = = PUNCT ejpam-3086 49 17 2φ 2φ PROPN ejpam-3086 49 18 . . PUNCT ejpam-3086 50 1 conformal conformal ADJ ejpam-3086 50 2 transformation transformation NOUN ejpam-3086 50 3 , , PUNCT ejpam-3086 50 4 holomorphic holomorphic ADJ ejpam-3086 50 5 map map NOUN ejpam-3086 50 6 and and CCONJ ejpam-3086 50 7 harmonic harmonic ADJ ejpam-3086 50 8 map map NOUN ejpam-3086 50 9 have have VERB ejpam-3086 50 10 many many ADJ ejpam-3086 50 11 applications application NOUN ejpam-3086 50 12 in in ADP ejpam-3086 50 13 physical physical ADJ ejpam-3086 50 14 problems problem NOUN ejpam-3086 50 15 , , PUNCT ejpam-3086 50 16 medical medical ADJ ejpam-3086 50 17 physics physics NOUN ejpam-3086 50 18 , , PUNCT ejpam-3086 50 19 engineering engineering NOUN ejpam-3086 50 20 and and CCONJ ejpam-3086 50 21 applied apply VERB ejpam-3086 50 22 science science NOUN ejpam-3086 50 23 . . PUNCT ejpam-3086 51 1 regarding regard VERB ejpam-3086 51 2 to to ADP ejpam-3086 51 3 the the DET ejpam-3086 51 4 importance importance NOUN ejpam-3086 51 5 of of ADP ejpam-3086 51 6 these these DET ejpam-3086 51 7 maps map NOUN ejpam-3086 51 8 , , PUNCT ejpam-3086 51 9 in in ADP ejpam-3086 51 10 this this DET ejpam-3086 51 11 study study NOUN ejpam-3086 51 12 , , PUNCT ejpam-3086 51 13 conformal conformal ADJ ejpam-3086 51 14 transformation transformation NOUN ejpam-3086 51 15 , , PUNCT ejpam-3086 51 16 holomorphic holomorphic ADJ ejpam-3086 51 17 map map NOUN ejpam-3086 51 18 and and CCONJ ejpam-3086 51 19 harmonic harmonic ADJ ejpam-3086 51 20 map map NOUN ejpam-3086 51 21 on on ADP ejpam-3086 51 22 these these DET ejpam-3086 51 23 manifolds manifold NOUN ejpam-3086 51 24 are be AUX ejpam-3086 51 25 considered consider VERB ejpam-3086 51 26 . . PUNCT ejpam-3086 52 1 3 3 X ejpam-3086 52 2 . . X ejpam-3086 53 1 some some DET ejpam-3086 53 2 results result NOUN ejpam-3086 53 3 on on ADP ejpam-3086 53 4 quasi quasi ADJ ejpam-3086 53 5 contact contact NOUN ejpam-3086 53 6 metric metric ADJ ejpam-3086 53 7 and and CCONJ ejpam-3086 53 8 nearly nearly ADV ejpam-3086 53 9 sasakian sasakian ADJ ejpam-3086 53 10 manifolds manifold NOUN ejpam-3086 53 11 there there PRON ejpam-3086 53 12 are be VERB ejpam-3086 53 13 some some DET ejpam-3086 53 14 important important ADJ ejpam-3086 53 15 properties property NOUN ejpam-3086 53 16 on on ADP ejpam-3086 53 17 quasi quasi ADJ ejpam-3086 53 18 contact contact NOUN ejpam-3086 53 19 metric metric ADJ ejpam-3086 53 20 and and CCONJ ejpam-3086 53 21 nearly nearly ADV ejpam-3086 53 22 sasakian sasakian ADJ ejpam-3086 53 23 manifolds manifold NOUN ejpam-3086 53 24 which which PRON ejpam-3086 53 25 we we PRON ejpam-3086 53 26 need need VERB ejpam-3086 53 27 for for ADP ejpam-3086 53 28 the the DET ejpam-3086 53 29 next next ADJ ejpam-3086 53 30 section section NOUN ejpam-3086 53 31 . . PUNCT ejpam-3086 54 1 in in ADP ejpam-3086 54 2 the the DET ejpam-3086 54 3 following follow VERB ejpam-3086 54 4 lemma lemma PROPN ejpam-3086 54 5 we we PRON ejpam-3086 54 6 list list VERB ejpam-3086 54 7 some some DET ejpam-3086 54 8 basic basic ADJ ejpam-3086 54 9 properties property NOUN ejpam-3086 54 10 of of ADP ejpam-3086 54 11 quasi quasi ADJ ejpam-3086 54 12 contact contact NOUN ejpam-3086 54 13 metric metric ADJ ejpam-3086 54 14 manifolds manifold NOUN ejpam-3086 54 15 which which PRON ejpam-3086 54 16 can can AUX ejpam-3086 54 17 be be AUX ejpam-3086 54 18 easily easily ADV ejpam-3086 54 19 proved prove VERB ejpam-3086 54 20 by by ADP ejpam-3086 54 21 using use VERB ejpam-3086 54 22 ( ( PUNCT ejpam-3086 54 23 1 1 NUM ejpam-3086 54 24 ) ) PUNCT ejpam-3086 54 25 ( ( PUNCT ejpam-3086 54 26 some some PRON ejpam-3086 54 27 of of ADP ejpam-3086 54 28 them they PRON ejpam-3086 54 29 are be AUX ejpam-3086 54 30 proved prove VERB ejpam-3086 54 31 in in ADP ejpam-3086 54 32 [ [ X ejpam-3086 54 33 3 3 NUM ejpam-3086 54 34 ] ] PUNCT ejpam-3086 54 35 and and CCONJ ejpam-3086 54 36 [ [ X ejpam-3086 54 37 10 10 NUM ejpam-3086 54 38 ] ] NUM ejpam-3086 54 39 ) ) PUNCT ejpam-3086 54 40 . . PUNCT ejpam-3086 55 1 lemma lemma PROPN ejpam-3086 55 2 1 1 X ejpam-3086 55 3 . . PUNCT ejpam-3086 56 1 in in ADP ejpam-3086 56 2 a a DET ejpam-3086 56 3 quasi quasi ADJ ejpam-3086 56 4 contact contact NOUN ejpam-3086 56 5 metric metric ADJ ejpam-3086 56 6 manifold manifold ADJ ejpam-3086 56 7 m m NOUN ejpam-3086 56 8 = = SYM ejpam-3086 56 9 ( ( PUNCT ejpam-3086 56 10 m m PROPN ejpam-3086 56 11 , , PUNCT ejpam-3086 56 12 φ φ PROPN ejpam-3086 56 13 , , PUNCT ejpam-3086 56 14 ξ ξ PROPN ejpam-3086 56 15 , , PUNCT ejpam-3086 56 16 η η NOUN ejpam-3086 56 17 , , PUNCT ejpam-3086 56 18 g g NOUN ejpam-3086 56 19 ) ) PUNCT ejpam-3086 56 20 the the DET ejpam-3086 56 21 following follow VERB ejpam-3086 56 22 properties property NOUN ejpam-3086 56 23 are be AUX ejpam-3086 56 24 hold hold NOUN ejpam-3086 56 25 ( ( PUNCT ejpam-3086 56 26 a)∇ξφ a)∇ξφ PROPN ejpam-3086 56 27 = = SYM ejpam-3086 56 28 0 0 NUM ejpam-3086 56 29 ( ( PUNCT ejpam-3086 56 30 b)∇ξξ b)∇ξξ PROPN ejpam-3086 56 31 = = SYM ejpam-3086 56 32 0 0 NUM ejpam-3086 56 33 ( ( PUNCT ejpam-3086 56 34 c)ηoh c)ηoh NOUN ejpam-3086 56 35 = = SYM ejpam-3086 56 36 0 0 NUM ejpam-3086 56 37 , , PUNCT ejpam-3086 56 38 hξ hξ NOUN ejpam-3086 56 39 = = SYM ejpam-3086 56 40 0 0 PUNCT ejpam-3086 56 41 ( ( PUNCT ejpam-3086 56 42 d)(∇xη)y d)(∇xη)y NOUN ejpam-3086 56 43 = = PUNCT ejpam-3086 56 44 g(x g(x PROPN ejpam-3086 56 45 + + CCONJ ejpam-3086 56 46 hx hx PROPN ejpam-3086 56 47 , , PUNCT ejpam-3086 56 48 φy φy PROPN ejpam-3086 56 49 ) ) PUNCT ejpam-3086 56 50 ( ( PUNCT ejpam-3086 56 51 e)φh+ e)φh+ NOUN ejpam-3086 56 52 hφ hφ PROPN ejpam-3086 56 53 = = NOUN ejpam-3086 56 54 0 0 PROPN ejpam-3086 56 55 . . PUNCT ejpam-3086 57 1 we we PRON ejpam-3086 57 2 know know VERB ejpam-3086 57 3 that that SCONJ ejpam-3086 57 4 in in ADP ejpam-3086 57 5 a a DET ejpam-3086 57 6 ( ( PUNCT ejpam-3086 57 7 φ φ PROPN ejpam-3086 57 8 , , PUNCT ejpam-3086 57 9 ξ ξ PROPN ejpam-3086 57 10 , , PUNCT ejpam-3086 57 11 η η NOUN ejpam-3086 57 12 , , PUNCT ejpam-3086 57 13 g g NOUN ejpam-3086 57 14 ) ) PUNCT ejpam-3086 57 15 contact contact NOUN ejpam-3086 57 16 metric metric ADJ ejpam-3086 57 17 manifold manifold NOUN ejpam-3086 57 18 , , PUNCT ejpam-3086 57 19 it it PRON ejpam-3086 57 20 satisfies satisfy VERB ejpam-3086 57 21 dη dη X ejpam-3086 57 22 = = SYM ejpam-3086 57 23 φ φ PROPN ejpam-3086 57 24 . . PUNCT ejpam-3086 58 1 it it PRON ejpam-3086 58 2 should should AUX ejpam-3086 58 3 be be AUX ejpam-3086 58 4 very very ADV ejpam-3086 58 5 useful useful ADJ ejpam-3086 58 6 if if SCONJ ejpam-3086 58 7 we we PRON ejpam-3086 58 8 have have VERB ejpam-3086 58 9 an an DET ejpam-3086 58 10 expression expression NOUN ejpam-3086 58 11 for for ADP ejpam-3086 58 12 dη dη NOUN ejpam-3086 58 13 with with ADP ejpam-3086 58 14 respect respect NOUN ejpam-3086 58 15 to to ADP ejpam-3086 58 16 φ φ PROPN ejpam-3086 58 17 in in ADP ejpam-3086 58 18 quasi quasi ADJ ejpam-3086 58 19 contact contact NOUN ejpam-3086 58 20 metric metric ADJ ejpam-3086 58 21 and and CCONJ ejpam-3086 58 22 nearly nearly ADV ejpam-3086 58 23 sasakian sasakian ADJ ejpam-3086 58 24 manifolds manifold NOUN ejpam-3086 58 25 . . PUNCT ejpam-3086 59 1 the the DET ejpam-3086 59 2 following follow VERB ejpam-3086 59 3 theorem theorem NOUN ejpam-3086 59 4 gives give VERB ejpam-3086 59 5 the the DET ejpam-3086 59 6 desired desire VERB ejpam-3086 59 7 formula formula NOUN ejpam-3086 59 8 , , PUNCT ejpam-3086 59 9 and and CCONJ ejpam-3086 59 10 then then ADV ejpam-3086 59 11 we we PRON ejpam-3086 59 12 give give VERB ejpam-3086 59 13 a a DET ejpam-3086 59 14 number number NOUN ejpam-3086 59 15 of of ADP ejpam-3086 59 16 important important ADJ ejpam-3086 59 17 properties property NOUN ejpam-3086 59 18 on on ADP ejpam-3086 59 19 these these DET ejpam-3086 59 20 manifolds manifold NOUN ejpam-3086 59 21 by by ADP ejpam-3086 59 22 using use VERB ejpam-3086 59 23 this this DET ejpam-3086 59 24 formula formula NOUN ejpam-3086 59 25 . . PUNCT ejpam-3086 60 1 theorem theorem NOUN ejpam-3086 60 2 1 1 NUM ejpam-3086 60 3 . . PUNCT ejpam-3086 61 1 in in ADP ejpam-3086 61 2 a a DET ejpam-3086 61 3 quasi quasi ADJ ejpam-3086 61 4 contact contact NOUN ejpam-3086 61 5 metric metric ADJ ejpam-3086 61 6 manifold manifold ADJ ejpam-3086 61 7 m m NOUN ejpam-3086 61 8 = = SYM ejpam-3086 61 9 ( ( PUNCT ejpam-3086 61 10 m m PROPN ejpam-3086 61 11 , , PUNCT ejpam-3086 61 12 φ φ PROPN ejpam-3086 61 13 , , PUNCT ejpam-3086 61 14 ξ ξ PROPN ejpam-3086 61 15 , , PUNCT ejpam-3086 61 16 η η NOUN ejpam-3086 61 17 , , PUNCT ejpam-3086 61 18 g g NOUN ejpam-3086 61 19 ) ) PUNCT ejpam-3086 61 20 we we PRON ejpam-3086 61 21 have have VERB ejpam-3086 61 22 dη(x dη(x NOUN ejpam-3086 61 23 , , PUNCT ejpam-3086 61 24 y y PROPN ejpam-3086 61 25 ) ) PUNCT ejpam-3086 61 26 = = SYM ejpam-3086 62 1 φ(x φ(x PROPN ejpam-3086 62 2 , , PUNCT ejpam-3086 62 3 y y PROPN ejpam-3086 62 4 ) ) PUNCT ejpam-3086 63 1 + + CCONJ ejpam-3086 63 2 1 1 NUM ejpam-3086 63 3 2 2 NUM ejpam-3086 63 4 [ [ X ejpam-3086 63 5 g(hx g(hx PROPN ejpam-3086 63 6 , , PUNCT ejpam-3086 63 7 φy φy NOUN ejpam-3086 63 8 ) ) PUNCT ejpam-3086 63 9 − − PROPN ejpam-3086 63 10 g(φx g(φx NOUN ejpam-3086 63 11 , , PUNCT ejpam-3086 63 12 hy hy NOUN ejpam-3086 63 13 ) ) PUNCT ejpam-3086 63 14 ] ] PUNCT ejpam-3086 63 15 . . PUNCT ejpam-3086 64 1 proof proof NOUN ejpam-3086 64 2 . . PUNCT ejpam-3086 65 1 using use VERB ejpam-3086 65 2 lemma lemma PROPN ejpam-3086 65 3 1(d 1(d NUM ejpam-3086 65 4 ) ) PUNCT ejpam-3086 65 5 , , PUNCT ejpam-3086 65 6 we we PRON ejpam-3086 65 7 have have VERB ejpam-3086 65 8 dη(x dη(x NOUN ejpam-3086 65 9 , , PUNCT ejpam-3086 65 10 y y PROPN ejpam-3086 65 11 ) ) PUNCT ejpam-3086 65 12 = = SYM ejpam-3086 66 1 1 1 NUM ejpam-3086 66 2 2 2 NUM ejpam-3086 66 3 [ [ X ejpam-3086 66 4 ( ( PUNCT ejpam-3086 66 5 ∇xη)y ∇xη)y NOUN ejpam-3086 66 6 − − PROPN ejpam-3086 66 7 ( ( PUNCT ejpam-3086 66 8 ∇y ∇y PROPN ejpam-3086 66 9 η)x η)x ADV ejpam-3086 66 10 ] ] X ejpam-3086 66 11 f. f. PROPN ejpam-3086 66 12 malek malek PROPN ejpam-3086 66 13 , , PUNCT ejpam-3086 66 14 m. m. NOUN ejpam-3086 66 15 samanipour samanipour PROPN ejpam-3086 66 16 / / SYM ejpam-3086 66 17 eur eur PROPN ejpam-3086 66 18 . . PUNCT ejpam-3086 67 1 j. j. PROPN ejpam-3086 67 2 pure pure PROPN ejpam-3086 67 3 appl appl PROPN ejpam-3086 67 4 . . PROPN ejpam-3086 67 5 math math PROPN ejpam-3086 67 6 , , PUNCT ejpam-3086 67 7 10 10 NUM ejpam-3086 67 8 ( ( PUNCT ejpam-3086 67 9 5 5 NUM ejpam-3086 67 10 ) ) PUNCT ejpam-3086 67 11 ( ( PUNCT ejpam-3086 67 12 2017 2017 NUM ejpam-3086 67 13 ) ) PUNCT ejpam-3086 67 14 , , PUNCT ejpam-3086 67 15 946 946 NUM ejpam-3086 67 16 - - SYM ejpam-3086 67 17 954 954 NUM ejpam-3086 67 18 949 949 NUM ejpam-3086 67 19 = = SYM ejpam-3086 67 20 1 1 NUM ejpam-3086 67 21 2 2 NUM ejpam-3086 67 22 [ [ X ejpam-3086 67 23 g(x g(x X ejpam-3086 67 24 + + CCONJ ejpam-3086 67 25 hx hx PROPN ejpam-3086 67 26 , , PUNCT ejpam-3086 67 27 φy φy NOUN ejpam-3086 67 28 ) ) PUNCT ejpam-3086 67 29 − − PROPN ejpam-3086 68 1 g(y g(y PROPN ejpam-3086 68 2 + + PROPN ejpam-3086 68 3 hy hy PROPN ejpam-3086 68 4 , , PUNCT ejpam-3086 68 5 φx φx NOUN ejpam-3086 68 6 ) ) PUNCT ejpam-3086 68 7 ] ] PUNCT ejpam-3086 69 1 = = PUNCT ejpam-3086 69 2 g(x g(x NOUN ejpam-3086 69 3 , , PUNCT ejpam-3086 69 4 φy φy NOUN ejpam-3086 69 5 ) ) PUNCT ejpam-3086 69 6 + + CCONJ ejpam-3086 69 7 1 1 NUM ejpam-3086 69 8 2 2 NUM ejpam-3086 69 9 [ [ X ejpam-3086 69 10 g(hx g(hx PROPN ejpam-3086 69 11 , , PUNCT ejpam-3086 69 12 φy φy NOUN ejpam-3086 69 13 ) ) PUNCT ejpam-3086 69 14 − − PROPN ejpam-3086 69 15 g(φx g(φx NOUN ejpam-3086 69 16 , , PUNCT ejpam-3086 69 17 hy hy NOUN ejpam-3086 69 18 ) ) PUNCT ejpam-3086 69 19 ] ] PUNCT ejpam-3086 69 20 . . PUNCT ejpam-3086 70 1 it it PRON ejpam-3086 70 2 is be AUX ejpam-3086 70 3 remarkable remarkable ADJ ejpam-3086 70 4 to to PART ejpam-3086 70 5 note note VERB ejpam-3086 70 6 that that SCONJ ejpam-3086 70 7 the the DET ejpam-3086 70 8 above above ADJ ejpam-3086 70 9 theorem theorem NOUN ejpam-3086 70 10 also also ADV ejpam-3086 70 11 shows show VERB ejpam-3086 70 12 that that SCONJ ejpam-3086 70 13 if if SCONJ ejpam-3086 70 14 h h NOUN ejpam-3086 70 15 is be AUX ejpam-3086 70 16 symmetric symmetric ADJ ejpam-3086 70 17 , , PUNCT ejpam-3086 70 18 then then ADV ejpam-3086 70 19 the the DET ejpam-3086 70 20 quasi quasi ADJ ejpam-3086 70 21 contact contact PROPN ejpam-3086 70 22 metric metric PROPN ejpam-3086 70 23 manifold manifold PROPN ejpam-3086 70 24 is be AUX ejpam-3086 70 25 contact contact NOUN ejpam-3086 70 26 metric metric NOUN ejpam-3086 70 27 . . PUNCT ejpam-3086 71 1 in in ADP ejpam-3086 71 2 nearly nearly ADV ejpam-3086 71 3 sasakian sasakian ADJ ejpam-3086 71 4 manifold manifold NOUN ejpam-3086 71 5 ( ( PUNCT ejpam-3086 71 6 m m PROPN ejpam-3086 71 7 , , PUNCT ejpam-3086 71 8 φ φ PROPN ejpam-3086 71 9 , , PUNCT ejpam-3086 71 10 ξ ξ PROPN ejpam-3086 71 11 , , PUNCT ejpam-3086 71 12 η η NOUN ejpam-3086 71 13 , , PUNCT ejpam-3086 71 14 g g NOUN ejpam-3086 71 15 ) ) PUNCT ejpam-3086 71 16 , , PUNCT ejpam-3086 71 17 a a DET ejpam-3086 71 18 tensor tensor NOUN ejpam-3086 71 19 field field NOUN ejpam-3086 71 20 h́ h́ NOUN ejpam-3086 71 21 of of ADP ejpam-3086 71 22 type type NOUN ejpam-3086 71 23 ( ( PUNCT ejpam-3086 71 24 1 1 NUM ejpam-3086 71 25 , , PUNCT ejpam-3086 71 26 1 1 NUM ejpam-3086 71 27 ) ) PUNCT ejpam-3086 71 28 is be AUX ejpam-3086 71 29 defined define VERB ejpam-3086 71 30 by by ADP ejpam-3086 71 31 ( ( PUNCT ejpam-3086 71 32 [ [ X ejpam-3086 71 33 5 5 NUM ejpam-3086 71 34 ] ] PUNCT ejpam-3086 71 35 ): ): PUNCT ejpam-3086 71 36 h́x h́x ADJ ejpam-3086 71 37 : : PUNCT ejpam-3086 71 38 = = SYM ejpam-3086 71 39 ∇xξ ∇xξ PROPN ejpam-3086 71 40 + + CCONJ ejpam-3086 71 41 φx φx VERB ejpam-3086 71 42 . . PUNCT ejpam-3086 72 1 it it PRON ejpam-3086 72 2 is be AUX ejpam-3086 72 3 skew skew ADJ ejpam-3086 72 4 - - PUNCT ejpam-3086 72 5 symmetric symmetric ADJ ejpam-3086 72 6 and and CCONJ ejpam-3086 72 7 anticommutes anticommute NOUN ejpam-3086 72 8 with with ADP ejpam-3086 72 9 φ φ PROPN ejpam-3086 72 10 . . PUNCT ejpam-3086 73 1 moreover moreover ADV ejpam-3086 73 2 , , PUNCT ejpam-3086 73 3 h́ξ h́ξ PROPN ejpam-3086 73 4 = = SYM ejpam-3086 73 5 0 0 PUNCT ejpam-3086 73 6 and and CCONJ ejpam-3086 73 7 ηoh́ ηoh́ NOUN ejpam-3086 73 8 = = SYM ejpam-3086 73 9 0 0 PUNCT ejpam-3086 73 10 ( ( PUNCT ejpam-3086 73 11 [ [ X ejpam-3086 73 12 5 5 NUM ejpam-3086 73 13 ] ] NUM ejpam-3086 73 14 ) ) PUNCT ejpam-3086 73 15 , , PUNCT ejpam-3086 73 16 and and CCONJ ejpam-3086 73 17 the the DET ejpam-3086 73 18 vanishing vanishing NOUN ejpam-3086 73 19 of of ADP ejpam-3086 73 20 h́ h́ PROPN ejpam-3086 73 21 causes cause VERB ejpam-3086 73 22 the the DET ejpam-3086 73 23 manifold manifold NOUN ejpam-3086 73 24 to to PART ejpam-3086 73 25 be be AUX ejpam-3086 73 26 sasakian sasakian ADJ ejpam-3086 73 27 ( ( PUNCT ejpam-3086 73 28 [ [ X ejpam-3086 73 29 13 13 NUM ejpam-3086 73 30 ] ] NUM ejpam-3086 73 31 ) ) PUNCT ejpam-3086 73 32 . . PUNCT ejpam-3086 74 1 theorem theorem NOUN ejpam-3086 74 2 2 2 NUM ejpam-3086 74 3 . . PUNCT ejpam-3086 75 1 in in ADP ejpam-3086 75 2 a a DET ejpam-3086 75 3 nearly nearly ADV ejpam-3086 75 4 sasakian sasakian ADJ ejpam-3086 75 5 manifold manifold ADJ ejpam-3086 75 6 m m NOUN ejpam-3086 75 7 = = SYM ejpam-3086 75 8 ( ( PUNCT ejpam-3086 75 9 m m PROPN ejpam-3086 75 10 , , PUNCT ejpam-3086 75 11 φ φ PROPN ejpam-3086 75 12 , , PUNCT ejpam-3086 75 13 ξ ξ PROPN ejpam-3086 75 14 , , PUNCT ejpam-3086 75 15 η η NOUN ejpam-3086 75 16 , , PUNCT ejpam-3086 75 17 g g NOUN ejpam-3086 75 18 ) ) PUNCT ejpam-3086 75 19 , , PUNCT ejpam-3086 75 20 we we PRON ejpam-3086 75 21 have have VERB ejpam-3086 75 22 dη(x dη(x NOUN ejpam-3086 75 23 , , PUNCT ejpam-3086 75 24 y y PROPN ejpam-3086 75 25 ) ) PUNCT ejpam-3086 76 1 = = SYM ejpam-3086 76 2 φ(x φ(x PROPN ejpam-3086 76 3 , , PUNCT ejpam-3086 76 4 y y PROPN ejpam-3086 76 5 ) ) PUNCT ejpam-3086 76 6 + + CCONJ ejpam-3086 76 7 g(h́x g(h́x PROPN ejpam-3086 76 8 , , PUNCT ejpam-3086 76 9 y y PROPN ejpam-3086 76 10 ) ) PUNCT ejpam-3086 76 11 . . PUNCT ejpam-3086 77 1 proof proof NOUN ejpam-3086 77 2 . . PUNCT ejpam-3086 78 1 we we PRON ejpam-3086 78 2 have have VERB ejpam-3086 78 3 dη(x dη(x PROPN ejpam-3086 78 4 , , PUNCT ejpam-3086 78 5 y y PROPN ejpam-3086 78 6 ) ) PUNCT ejpam-3086 78 7 = = SYM ejpam-3086 79 1 1 1 NUM ejpam-3086 79 2 2 2 NUM ejpam-3086 79 3 [ [ X ejpam-3086 79 4 ( ( PUNCT ejpam-3086 79 5 ∇xη)y ∇xη)y NOUN ejpam-3086 79 6 − − PROPN ejpam-3086 79 7 ( ( PUNCT ejpam-3086 79 8 ∇y ∇y PROPN ejpam-3086 79 9 η)x η)x ADV ejpam-3086 79 10 ] ] X ejpam-3086 79 11 = = SYM ejpam-3086 79 12 1 1 NUM ejpam-3086 79 13 2 2 NUM ejpam-3086 79 14 [ [ X ejpam-3086 79 15 g(∇xξ g(∇xξ PROPN ejpam-3086 79 16 , , PUNCT ejpam-3086 79 17 y y PROPN ejpam-3086 79 18 ) ) PUNCT ejpam-3086 79 19 − − PROPN ejpam-3086 79 20 g(∇y g(∇y NOUN ejpam-3086 79 21 ξ ξ X ejpam-3086 79 22 , , PUNCT ejpam-3086 79 23 x x NOUN ejpam-3086 79 24 ) ) PUNCT ejpam-3086 79 25 ] ] PUNCT ejpam-3086 80 1 = = SYM ejpam-3086 80 2 1 1 NUM ejpam-3086 80 3 2 2 NUM ejpam-3086 80 4 [ [ X ejpam-3086 80 5 g(−φx g(−φx NOUN ejpam-3086 80 6 + + CCONJ ejpam-3086 80 7 h́x h́x ADJ ejpam-3086 80 8 , , PUNCT ejpam-3086 80 9 y y NOUN ejpam-3086 80 10 ) ) PUNCT ejpam-3086 80 11 − − PROPN ejpam-3086 81 1 g(−φy g(−φy NOUN ejpam-3086 81 2 + + CCONJ ejpam-3086 81 3 h́ h́ NOUN ejpam-3086 81 4 y y PROPN ejpam-3086 81 5 , , PUNCT ejpam-3086 81 6 x x NOUN ejpam-3086 81 7 ) ) PUNCT ejpam-3086 81 8 ] ] PUNCT ejpam-3086 82 1 = = SYM ejpam-3086 82 2 φ(x φ(x PROPN ejpam-3086 82 3 , , PUNCT ejpam-3086 82 4 y y PROPN ejpam-3086 82 5 ) ) PUNCT ejpam-3086 82 6 + + CCONJ ejpam-3086 82 7 g(h́x g(h́x PROPN ejpam-3086 82 8 , , PUNCT ejpam-3086 82 9 y y PROPN ejpam-3086 82 10 ) ) PUNCT ejpam-3086 82 11 . . PUNCT ejpam-3086 83 1 lemma lemma PROPN ejpam-3086 83 2 2 2 X ejpam-3086 83 3 . . PUNCT ejpam-3086 84 1 in in ADP ejpam-3086 84 2 a a DET ejpam-3086 84 3 quasi quasi ADJ ejpam-3086 84 4 contact contact NOUN ejpam-3086 84 5 metric metric NOUN ejpam-3086 84 6 ( ( PUNCT ejpam-3086 84 7 or or CCONJ ejpam-3086 84 8 nearly nearly ADV ejpam-3086 84 9 sasakian sasakian ADJ ejpam-3086 84 10 ) ) PUNCT ejpam-3086 84 11 manifold manifold ADJ ejpam-3086 84 12 m m NOUN ejpam-3086 84 13 = = SYM ejpam-3086 84 14 ( ( PUNCT ejpam-3086 84 15 m m PROPN ejpam-3086 84 16 , , PUNCT ejpam-3086 84 17 φ φ PROPN ejpam-3086 84 18 , , PUNCT ejpam-3086 84 19 ξ ξ PROPN ejpam-3086 84 20 , , PUNCT ejpam-3086 84 21 η η NOUN ejpam-3086 84 22 , , PUNCT ejpam-3086 84 23 g g NOUN ejpam-3086 84 24 ) ) PUNCT ejpam-3086 84 25 we we PRON ejpam-3086 84 26 have have VERB ejpam-3086 84 27 dη(φx dη(φx NOUN ejpam-3086 84 28 , , PUNCT ejpam-3086 84 29 φy φy NOUN ejpam-3086 84 30 ) ) PUNCT ejpam-3086 85 1 + + CCONJ ejpam-3086 85 2 dη(x dη(x PROPN ejpam-3086 85 3 , , PUNCT ejpam-3086 85 4 y y PROPN ejpam-3086 85 5 ) ) PUNCT ejpam-3086 85 6 = = SYM ejpam-3086 86 1 2φ(x 2φ(x NUM ejpam-3086 86 2 , , PUNCT ejpam-3086 86 3 y y PROPN ejpam-3086 86 4 ) ) PUNCT ejpam-3086 86 5 . . PUNCT ejpam-3086 87 1 proof proof NOUN ejpam-3086 87 2 . . PUNCT ejpam-3086 88 1 by by ADP ejpam-3086 88 2 theorem theorem NOUN ejpam-3086 88 3 1 1 NUM ejpam-3086 88 4 we we PRON ejpam-3086 88 5 have have VERB ejpam-3086 88 6 : : PUNCT ejpam-3086 88 7 dη(φx dη(φx ADV ejpam-3086 88 8 , , PUNCT ejpam-3086 88 9 φy φy NOUN ejpam-3086 88 10 ) ) PUNCT ejpam-3086 88 11 + + CCONJ ejpam-3086 88 12 dη(x dη(x PROPN ejpam-3086 88 13 , , PUNCT ejpam-3086 88 14 y y PROPN ejpam-3086 88 15 ) ) PUNCT ejpam-3086 88 16 = = PUNCT ejpam-3086 89 1 φ(φx φ(φx SYM ejpam-3086 89 2 , , PUNCT ejpam-3086 89 3 φy φy NOUN ejpam-3086 89 4 ) ) PUNCT ejpam-3086 89 5 + + CCONJ ejpam-3086 89 6 1 1 NUM ejpam-3086 89 7 2 2 NUM ejpam-3086 89 8 [ [ X ejpam-3086 89 9 φ(hφx φ(hφx ADJ ejpam-3086 89 10 , , PUNCT ejpam-3086 89 11 φy φy INTJ ejpam-3086 89 12 ) ) PUNCT ejpam-3086 89 13 + + CCONJ ejpam-3086 89 14 φ(φx φ(φx ADP ejpam-3086 89 15 , , PUNCT ejpam-3086 89 16 hφy hφy NOUN ejpam-3086 89 17 ) ) PUNCT ejpam-3086 89 18 ] ] PUNCT ejpam-3086 90 1 + + PUNCT ejpam-3086 90 2 φ(x φ(x PROPN ejpam-3086 90 3 , , PUNCT ejpam-3086 90 4 y y PROPN ejpam-3086 90 5 ) ) PUNCT ejpam-3086 90 6 + + CCONJ ejpam-3086 90 7 1 1 NUM ejpam-3086 90 8 2 2 NUM ejpam-3086 90 9 [ [ X ejpam-3086 90 10 φ(hx φ(hx PROPN ejpam-3086 90 11 , , PUNCT ejpam-3086 90 12 y y PROPN ejpam-3086 90 13 ) ) PUNCT ejpam-3086 91 1 + + CCONJ ejpam-3086 91 2 φ(x φ(x PROPN ejpam-3086 91 3 , , PUNCT ejpam-3086 91 4 hy hy NOUN ejpam-3086 91 5 ) ) PUNCT ejpam-3086 91 6 ] ] PUNCT ejpam-3086 92 1 = = PUNCT ejpam-3086 92 2 2φ(x 2φ(x NUM ejpam-3086 92 3 , , PUNCT ejpam-3086 92 4 y y PROPN ejpam-3086 92 5 ) ) PUNCT ejpam-3086 93 1 + + CCONJ ejpam-3086 93 2 1 1 NUM ejpam-3086 93 3 2 2 NUM ejpam-3086 93 4 [ [ X ejpam-3086 93 5 −φ(hx −φ(hx X ejpam-3086 93 6 , , PUNCT ejpam-3086 93 7 y y PROPN ejpam-3086 93 8 ) ) PUNCT ejpam-3086 93 9 − − PROPN ejpam-3086 94 1 φ(x φ(x PROPN ejpam-3086 94 2 , , PUNCT ejpam-3086 94 3 hy hy NOUN ejpam-3086 94 4 ) ) PUNCT ejpam-3086 95 1 + + NOUN ejpam-3086 95 2 φ(hx φ(hx PROPN ejpam-3086 95 3 , , PUNCT ejpam-3086 95 4 y y PROPN ejpam-3086 95 5 ) ) PUNCT ejpam-3086 96 1 + + CCONJ ejpam-3086 96 2 φ(x φ(x PROPN ejpam-3086 96 3 , , PUNCT ejpam-3086 96 4 hy hy NOUN ejpam-3086 96 5 ) ) PUNCT ejpam-3086 96 6 ] ] PUNCT ejpam-3086 97 1 = = PUNCT ejpam-3086 97 2 2φ(x 2φ(x NUM ejpam-3086 97 3 , , PUNCT ejpam-3086 97 4 y y PROPN ejpam-3086 97 5 ) ) PUNCT ejpam-3086 97 6 . . PUNCT ejpam-3086 98 1 ( ( PUNCT ejpam-3086 98 2 by by ADP ejpam-3086 98 3 theorem theorem NOUN ejpam-3086 98 4 2 2 NUM ejpam-3086 98 5 and and CCONJ ejpam-3086 98 6 applying apply VERB ejpam-3086 98 7 the the DET ejpam-3086 98 8 same same ADJ ejpam-3086 98 9 technique technique NOUN ejpam-3086 98 10 the the DET ejpam-3086 98 11 result result NOUN ejpam-3086 98 12 for for ADP ejpam-3086 98 13 nearly nearly ADV ejpam-3086 98 14 sasakian sasakian ADJ ejpam-3086 98 15 manifolds manifold NOUN ejpam-3086 98 16 follows follow VERB ejpam-3086 98 17 . . PUNCT ejpam-3086 98 18 ) ) PUNCT ejpam-3086 99 1 theorems theorem VERB ejpam-3086 99 2 1 1 NUM ejpam-3086 99 3 and and CCONJ ejpam-3086 99 4 2 2 NUM ejpam-3086 99 5 , , PUNCT ejpam-3086 99 6 show show VERB ejpam-3086 99 7 that that SCONJ ejpam-3086 99 8 dη(x dη(x NOUN ejpam-3086 99 9 , , PUNCT ejpam-3086 99 10 ξ ξ X ejpam-3086 99 11 ) ) PUNCT ejpam-3086 99 12 = = SYM ejpam-3086 99 13 0 0 NUM ejpam-3086 99 14 , , PUNCT ejpam-3086 99 15 and and CCONJ ejpam-3086 99 16 then then ADV ejpam-3086 99 17 we we PRON ejpam-3086 99 18 deduce deduce VERB ejpam-3086 99 19 : : PUNCT ejpam-3086 99 20 f. f. PROPN ejpam-3086 99 21 malek malek PROPN ejpam-3086 99 22 , , PUNCT ejpam-3086 99 23 m. m. NOUN ejpam-3086 99 24 samanipour samanipour PROPN ejpam-3086 99 25 / / SYM ejpam-3086 99 26 eur eur PROPN ejpam-3086 99 27 . . PUNCT ejpam-3086 100 1 j. j. PROPN ejpam-3086 100 2 pure pure PROPN ejpam-3086 100 3 appl appl PROPN ejpam-3086 100 4 . . PROPN ejpam-3086 100 5 math math PROPN ejpam-3086 100 6 , , PUNCT ejpam-3086 100 7 10 10 NUM ejpam-3086 100 8 ( ( PUNCT ejpam-3086 100 9 5 5 NUM ejpam-3086 100 10 ) ) PUNCT ejpam-3086 100 11 ( ( PUNCT ejpam-3086 100 12 2017 2017 NUM ejpam-3086 100 13 ) ) PUNCT ejpam-3086 100 14 , , PUNCT ejpam-3086 100 15 946 946 NUM ejpam-3086 100 16 - - SYM ejpam-3086 100 17 954 954 NUM ejpam-3086 100 18 950 950 NUM ejpam-3086 100 19 corollary corollary NOUN ejpam-3086 100 20 1 1 NUM ejpam-3086 100 21 . . PUNCT ejpam-3086 101 1 in in ADP ejpam-3086 101 2 a a DET ejpam-3086 101 3 ( ( PUNCT ejpam-3086 101 4 φ φ PROPN ejpam-3086 101 5 , , PUNCT ejpam-3086 101 6 ξ ξ PROPN ejpam-3086 101 7 , , PUNCT ejpam-3086 101 8 η η PROPN ejpam-3086 101 9 , , PUNCT ejpam-3086 101 10 g)quasi g)quasi PROPN ejpam-3086 101 11 contact contact NOUN ejpam-3086 101 12 metric metric NOUN ejpam-3086 101 13 ( ( PUNCT ejpam-3086 101 14 or or CCONJ ejpam-3086 101 15 nearly nearly ADV ejpam-3086 101 16 sasakian sasakian ADJ ejpam-3086 101 17 ) ) PUNCT ejpam-3086 101 18 manifolds manifold NOUN ejpam-3086 101 19 , , PUNCT ejpam-3086 101 20 ξ ξ PROPN ejpam-3086 101 21 ∈ ∈ PROPN ejpam-3086 101 22 kerdη kerdη PROPN ejpam-3086 101 23 . . PUNCT ejpam-3086 102 1 theorem theorem NOUN ejpam-3086 102 2 3 3 NUM ejpam-3086 102 3 . . PUNCT ejpam-3086 103 1 in in ADP ejpam-3086 103 2 a a DET ejpam-3086 103 3 quasi quasi ADJ ejpam-3086 103 4 contact contact NOUN ejpam-3086 103 5 metric metric NOUN ejpam-3086 103 6 ( ( PUNCT ejpam-3086 103 7 or or CCONJ ejpam-3086 103 8 nearly nearly ADV ejpam-3086 103 9 sasakian sasakian ADJ ejpam-3086 103 10 ) ) PUNCT ejpam-3086 103 11 manifold manifold ADJ ejpam-3086 103 12 m m NOUN ejpam-3086 103 13 = = SYM ejpam-3086 103 14 ( ( PUNCT ejpam-3086 103 15 m m PROPN ejpam-3086 103 16 , , PUNCT ejpam-3086 103 17 φ φ PROPN ejpam-3086 103 18 , , PUNCT ejpam-3086 103 19 ξ ξ PROPN ejpam-3086 103 20 , , PUNCT ejpam-3086 103 21 η η NOUN ejpam-3086 103 22 , , PUNCT ejpam-3086 103 23 g g NOUN ejpam-3086 103 24 ) ) PUNCT ejpam-3086 103 25 , , PUNCT ejpam-3086 103 26 η η PROPN ejpam-3086 103 27 is be AUX ejpam-3086 103 28 a a DET ejpam-3086 103 29 contact contact NOUN ejpam-3086 103 30 form form NOUN ejpam-3086 103 31 . . PUNCT ejpam-3086 104 1 proof proof NOUN ejpam-3086 104 2 . . PUNCT ejpam-3086 105 1 let let VERB ejpam-3086 105 2 m m VERB ejpam-3086 105 3 = = SYM ejpam-3086 105 4 ( ( PUNCT ejpam-3086 105 5 m m PROPN ejpam-3086 105 6 , , PUNCT ejpam-3086 105 7 φ φ PROPN ejpam-3086 105 8 , , PUNCT ejpam-3086 105 9 ξ ξ PROPN ejpam-3086 105 10 , , PUNCT ejpam-3086 105 11 η η NOUN ejpam-3086 105 12 , , PUNCT ejpam-3086 105 13 g g NOUN ejpam-3086 105 14 ) ) PUNCT ejpam-3086 105 15 be be VERB ejpam-3086 105 16 a a DET ejpam-3086 105 17 ( ( PUNCT ejpam-3086 105 18 2n+1)-dimensional 2n+1)-dimensional NUM ejpam-3086 105 19 quasi quasi ADJ ejpam-3086 105 20 contact contact NOUN ejpam-3086 105 21 metric metric NOUN ejpam-3086 105 22 ( ( PUNCT ejpam-3086 105 23 or or CCONJ ejpam-3086 105 24 nearly nearly ADV ejpam-3086 105 25 sasakain sasakain NOUN ejpam-3086 105 26 ) ) PUNCT ejpam-3086 105 27 manifold manifold ADJ ejpam-3086 105 28 . . PUNCT ejpam-3086 106 1 we we PRON ejpam-3086 106 2 prove prove VERB ejpam-3086 106 3 that that SCONJ ejpam-3086 106 4 rankdη rankdη NOUN ejpam-3086 106 5 = = SYM ejpam-3086 106 6 2n 2n NUM ejpam-3086 106 7 . . PUNCT ejpam-3086 107 1 let let VERB ejpam-3086 107 2 p p PRON ejpam-3086 107 3 ∈ ∈ PROPN ejpam-3086 107 4 m m NOUN ejpam-3086 107 5 and and CCONJ ejpam-3086 107 6 x⊥ξp x⊥ξp PROPN ejpam-3086 107 7 be be AUX ejpam-3086 107 8 a a DET ejpam-3086 107 9 nonzero nonzero ADJ ejpam-3086 107 10 vector vector NOUN ejpam-3086 107 11 in in ADP ejpam-3086 107 12 tpm tpm PROPN ejpam-3086 107 13 . . PUNCT ejpam-3086 108 1 if if SCONJ ejpam-3086 108 2 x x SYM ejpam-3086 108 3 ∈ ∈ PROPN ejpam-3086 108 4 kerdη kerdη NOUN ejpam-3086 108 5 then then ADV ejpam-3086 108 6 dη(x dη(x PROPN ejpam-3086 108 7 , , PUNCT ejpam-3086 108 8 . . PUNCT ejpam-3086 108 9 ) ) PUNCT ejpam-3086 109 1 = = PUNCT ejpam-3086 109 2 0 0 X ejpam-3086 109 3 . . PUNCT ejpam-3086 109 4 thus thus ADV ejpam-3086 109 5 by by ADP ejpam-3086 109 6 lemma lemma PROPN ejpam-3086 109 7 3.4 3.4 NUM ejpam-3086 109 8 , , PUNCT ejpam-3086 109 9 we we PRON ejpam-3086 109 10 have have VERB ejpam-3086 109 11 0 0 NUM ejpam-3086 109 12 = = NOUN ejpam-3086 109 13 dη(x dη(x NOUN ejpam-3086 109 14 , , PUNCT ejpam-3086 109 15 φx φx NOUN ejpam-3086 109 16 ) ) PUNCT ejpam-3086 109 17 = = SYM ejpam-3086 110 1 φ(x φ(x NOUN ejpam-3086 110 2 , , PUNCT ejpam-3086 110 3 φx φx NOUN ejpam-3086 110 4 ) ) PUNCT ejpam-3086 110 5 = = SYM ejpam-3086 110 6 −|x|2 −|x|2 PROPN ejpam-3086 110 7 , , PUNCT ejpam-3086 110 8 which which PRON ejpam-3086 110 9 is be AUX ejpam-3086 110 10 a a DET ejpam-3086 110 11 contradiction contradiction NOUN ejpam-3086 110 12 . . PUNCT ejpam-3086 111 1 thus thus ADV ejpam-3086 111 2 dim(kerdη dim(kerdη NOUN ejpam-3086 111 3 ) ) PUNCT ejpam-3086 111 4 ≤ ≤ NUM ejpam-3086 111 5 1 1 NUM ejpam-3086 111 6 . . PUNCT ejpam-3086 111 7 also also ADV ejpam-3086 111 8 by by ADP ejpam-3086 111 9 corollary corollary ADJ ejpam-3086 111 10 1 1 NUM ejpam-3086 111 11 we we PRON ejpam-3086 111 12 have have VERB ejpam-3086 111 13 , , PUNCT ejpam-3086 111 14 ξ ξ PROPN ejpam-3086 111 15 ∈ ∈ PROPN ejpam-3086 111 16 kerdη kerdη NOUN ejpam-3086 111 17 , , PUNCT ejpam-3086 111 18 and and CCONJ ejpam-3086 111 19 then then ADV ejpam-3086 111 20 dim(kerdη dim(kerdη X ejpam-3086 111 21 ) ) PUNCT ejpam-3086 111 22 = = SYM ejpam-3086 111 23 1 1 NUM ejpam-3086 111 24 , , PUNCT ejpam-3086 111 25 that that PRON ejpam-3086 111 26 results result VERB ejpam-3086 111 27 rankdη rankdη NOUN ejpam-3086 111 28 = = SYM ejpam-3086 111 29 2n 2n NUM ejpam-3086 111 30 . . PUNCT ejpam-3086 112 1 thus thus ADV ejpam-3086 112 2 η η PROPN ejpam-3086 112 3 ∧ ∧ PROPN ejpam-3086 112 4 ( ( PUNCT ejpam-3086 112 5 dη)n dη)n PROPN ejpam-3086 112 6 6= 6= ADP ejpam-3086 112 7 0 0 NUM ejpam-3086 112 8 on on ADP ejpam-3086 112 9 tpm tpm PROPN ejpam-3086 112 10 and and CCONJ ejpam-3086 112 11 the the DET ejpam-3086 112 12 proof proof NOUN ejpam-3086 112 13 is be AUX ejpam-3086 112 14 completed complete VERB ejpam-3086 112 15 . . PUNCT ejpam-3086 113 1 4 4 X ejpam-3086 113 2 . . X ejpam-3086 113 3 harmonic harmonic PROPN ejpam-3086 113 4 and and CCONJ ejpam-3086 113 5 ( ( PUNCT ejpam-3086 113 6 φ φ PROPN ejpam-3086 113 7 , , PUNCT ejpam-3086 113 8 φ́)-holomorphic φ́)-holomorphic ADJ ejpam-3086 113 9 maps map NOUN ejpam-3086 113 10 on on ADP ejpam-3086 113 11 quasi quasi ADJ ejpam-3086 113 12 contact contact NOUN ejpam-3086 113 13 metric metric NOUN ejpam-3086 113 14 , , PUNCT ejpam-3086 113 15 and and CCONJ ejpam-3086 113 16 nearly nearly ADV ejpam-3086 113 17 sasakian sasakian ADJ ejpam-3086 113 18 manifolds manifold NOUN ejpam-3086 113 19 it it PRON ejpam-3086 113 20 is be AUX ejpam-3086 113 21 known know VERB ejpam-3086 113 22 that that SCONJ ejpam-3086 113 23 a a DET ejpam-3086 113 24 contact contact NOUN ejpam-3086 113 25 manifold manifold ADJ ejpam-3086 113 26 with with ADP ejpam-3086 113 27 contact contact NOUN ejpam-3086 113 28 form form NOUN ejpam-3086 113 29 η η PROPN ejpam-3086 113 30 carries carry VERB ejpam-3086 113 31 an an DET ejpam-3086 113 32 associated associate VERB ejpam-3086 113 33 almost almost ADV ejpam-3086 113 34 contact contact NOUN ejpam-3086 113 35 metric metric ADJ ejpam-3086 113 36 structure structure NOUN ejpam-3086 113 37 ( ( PUNCT ejpam-3086 113 38 φ φ PROPN ejpam-3086 113 39 , , PUNCT ejpam-3086 113 40 ξ ξ PROPN ejpam-3086 113 41 , , PUNCT ejpam-3086 113 42 η η NOUN ejpam-3086 113 43 , , PUNCT ejpam-3086 113 44 g g NOUN ejpam-3086 113 45 ) ) PUNCT ejpam-3086 113 46 with with ADP ejpam-3086 113 47 φ φ PROPN ejpam-3086 113 48 = = SYM ejpam-3086 113 49 dη dη PROPN ejpam-3086 113 50 , , PUNCT ejpam-3086 113 51 called call VERB ejpam-3086 113 52 a a DET ejpam-3086 113 53 contact contact NOUN ejpam-3086 113 54 metric metric ADJ ejpam-3086 113 55 structure structure NOUN ejpam-3086 113 56 , , PUNCT ejpam-3086 113 57 but but CCONJ ejpam-3086 113 58 in in ADP ejpam-3086 113 59 this this DET ejpam-3086 113 60 section section NOUN ejpam-3086 113 61 , , PUNCT ejpam-3086 113 62 we we PRON ejpam-3086 113 63 consider consider VERB ejpam-3086 113 64 almost almost ADV ejpam-3086 113 65 contact contact VERB ejpam-3086 113 66 metric metric ADJ ejpam-3086 113 67 manifolds manifold NOUN ejpam-3086 113 68 in in ADP ejpam-3086 113 69 which which PRON ejpam-3086 113 70 dη+ dη+ NOUN ejpam-3086 113 71 dηoφ⊗ dηoφ⊗ PROPN ejpam-3086 113 72 φ φ PROPN ejpam-3086 113 73 = = SYM ejpam-3086 113 74 2φ 2φ NOUN ejpam-3086 113 75 and and CCONJ ejpam-3086 113 76 treat treat VERB ejpam-3086 113 77 conformal conformal ADJ ejpam-3086 113 78 transfomations transfomation NOUN ejpam-3086 113 79 and and CCONJ ejpam-3086 113 80 holomorphic holomorphic ADJ ejpam-3086 113 81 maps map NOUN ejpam-3086 113 82 on on ADP ejpam-3086 113 83 these these DET ejpam-3086 113 84 kind kind NOUN ejpam-3086 113 85 of of ADP ejpam-3086 113 86 manifolds manifold NOUN ejpam-3086 113 87 . . PUNCT ejpam-3086 114 1 let let VERB ejpam-3086 114 2 ( ( PUNCT ejpam-3086 114 3 m m NOUN ejpam-3086 114 4 , , PUNCT ejpam-3086 114 5 g,∇ g,∇ PROPN ejpam-3086 114 6 ) ) PUNCT ejpam-3086 114 7 and and CCONJ ejpam-3086 114 8 ( ( PUNCT ejpam-3086 114 9 m,́ m,́ PROPN ejpam-3086 114 10 ǵ ǵ PROPN ejpam-3086 114 11 , , PUNCT ejpam-3086 114 12 ∇́ ∇́ PROPN ejpam-3086 114 13 ) ) PUNCT ejpam-3086 114 14 be be VERB ejpam-3086 114 15 two two NUM ejpam-3086 114 16 riemannian riemannian ADJ ejpam-3086 114 17 manifolds manifold NOUN ejpam-3086 114 18 in in ADP ejpam-3086 114 19 which which PRON ejpam-3086 114 20 ∇ ∇ PROPN ejpam-3086 114 21 and and CCONJ ejpam-3086 114 22 ∇́ ∇́ PROPN ejpam-3086 114 23 are be AUX ejpam-3086 114 24 the the DET ejpam-3086 114 25 levi levi PROPN ejpam-3086 114 26 - - PUNCT ejpam-3086 114 27 civita civita NOUN ejpam-3086 114 28 connections connection NOUN ejpam-3086 114 29 on on ADP ejpam-3086 114 30 m m NOUN ejpam-3086 114 31 and and CCONJ ejpam-3086 114 32 m´respectively m´respectively ADV ejpam-3086 114 33 . . PUNCT ejpam-3086 115 1 for for ADP ejpam-3086 115 2 a a DET ejpam-3086 115 3 differentiable differentiable ADJ ejpam-3086 115 4 map map NOUN ejpam-3086 115 5 f f X ejpam-3086 115 6 : : PUNCT ejpam-3086 115 7 m m PROPN ejpam-3086 115 8 → → SYM ejpam-3086 115 9 m m NOUN ejpam-3086 115 10 ´ ´ NOUN ejpam-3086 115 11 between between ADP ejpam-3086 115 12 riemannian riemannian NOUN ejpam-3086 115 13 manifolds manifold VERB ejpam-3086 115 14 its its PRON ejpam-3086 115 15 tension tension NOUN ejpam-3086 115 16 field field NOUN ejpam-3086 115 17 τ(f τ(f NOUN ejpam-3086 115 18 ) ) PUNCT ejpam-3086 115 19 is be AUX ejpam-3086 115 20 the the DET ejpam-3086 115 21 trace trace NOUN ejpam-3086 115 22 of of ADP ejpam-3086 115 23 the the DET ejpam-3086 115 24 second second ADJ ejpam-3086 115 25 fundamental fundamental ADJ ejpam-3086 115 26 form form NOUN ejpam-3086 115 27 bf bf NOUN ejpam-3086 115 28 of of ADP ejpam-3086 115 29 f f PROPN ejpam-3086 115 30 : : PUNCT ejpam-3086 115 31 τ(f τ(f PROPN ejpam-3086 115 32 ) ) PUNCT ejpam-3086 115 33 : : PUNCT ejpam-3086 115 34 = = SYM ejpam-3086 115 35 σibf σibf NOUN ejpam-3086 115 36 ( ( PUNCT ejpam-3086 115 37 ei ei NOUN ejpam-3086 115 38 , , PUNCT ejpam-3086 115 39 ei ei NOUN ejpam-3086 115 40 ) ) PUNCT ejpam-3086 115 41 = = PUNCT ejpam-3086 115 42 σi(∇f σi(∇f NOUN ejpam-3086 115 43 −1tḿ −1tḿ NOUN ejpam-3086 115 44 ei ei NOUN ejpam-3086 115 45 df(ei)− df(ei)− PROPN ejpam-3086 115 46 df(∇eiei df(∇eiei PROPN ejpam-3086 115 47 ) ) PUNCT ejpam-3086 115 48 ) ) PUNCT ejpam-3086 115 49 , , PUNCT ejpam-3086 115 50 ( ( PUNCT ejpam-3086 115 51 3 3 X ejpam-3086 115 52 ) ) PUNCT ejpam-3086 115 53 where where SCONJ ejpam-3086 115 54 { { PUNCT ejpam-3086 115 55 ei ei AUX ejpam-3086 115 56 } } PUNCT ejpam-3086 115 57 is be AUX ejpam-3086 115 58 an an DET ejpam-3086 115 59 orthonormal orthonormal ADJ ejpam-3086 115 60 basis basis NOUN ejpam-3086 115 61 for for ADP ejpam-3086 115 62 the the DET ejpam-3086 115 63 tangent tangent ADJ ejpam-3086 115 64 space space NOUN ejpam-3086 115 65 txm txm PROPN ejpam-3086 115 66 at at ADP ejpam-3086 115 67 x x X ejpam-3086 115 68 ∈m ∈m NOUN ejpam-3086 115 69 , , PUNCT ejpam-3086 115 70 and and CCONJ ejpam-3086 115 71 ∇f−1tḿ ∇f−1tḿ NOUN ejpam-3086 115 72 denotes denote VERB ejpam-3086 115 73 the the DET ejpam-3086 115 74 pull pull NOUN ejpam-3086 115 75 - - PUNCT ejpam-3086 115 76 back back NOUN ejpam-3086 115 77 of of ADP ejpam-3086 115 78 the the DET ejpam-3086 115 79 levi levi PROPN ejpam-3086 115 80 - - PUNCT ejpam-3086 115 81 civita civita PROPN ejpam-3086 115 82 connection connection NOUN ejpam-3086 115 83 ∇́ ∇́ PROPN ejpam-3086 115 84 on on ADP ejpam-3086 115 85 m m PROPN ejpam-3086 115 86 ´ ´ NOUN ejpam-3086 115 87 to to ADP ejpam-3086 115 88 the the DET ejpam-3086 115 89 pull pull VERB ejpam-3086 115 90 - - PUNCT ejpam-3086 115 91 back back NOUN ejpam-3086 115 92 bundle bundle NOUN ejpam-3086 115 93 f−1tm´−→m f−1tm´−→m NUM ejpam-3086 115 94 , , PUNCT ejpam-3086 115 95 and and CCONJ ejpam-3086 115 96 df df NOUN ejpam-3086 115 97 : : PUNCT ejpam-3086 115 98 tm tm PROPN ejpam-3086 115 99 −→ −→ NOUN ejpam-3086 115 100 f−1tm´is f−1tm´i VERB ejpam-3086 115 101 the the DET ejpam-3086 115 102 differential differential NOUN ejpam-3086 115 103 of of ADP ejpam-3086 115 104 f f PROPN ejpam-3086 115 105 . . PUNCT ejpam-3086 116 1 definition definition NOUN ejpam-3086 116 2 1 1 NUM ejpam-3086 116 3 . . PUNCT ejpam-3086 117 1 ( ( PUNCT ejpam-3086 117 2 [ [ X ejpam-3086 117 3 8 8 NUM ejpam-3086 117 4 ] ] SYM ejpam-3086 117 5 ) ) PUNCT ejpam-3086 117 6 a a DET ejpam-3086 117 7 differentiable differentiable ADJ ejpam-3086 117 8 map map NOUN ejpam-3086 118 1 f f X ejpam-3086 118 2 : : PUNCT ejpam-3086 118 3 m m AUX ejpam-3086 118 4 → → SYM ejpam-3086 118 5 m´between m´between ADJ ejpam-3086 118 6 riemannian riemannian ADJ ejpam-3086 118 7 manifolds manifold NOUN ejpam-3086 118 8 m m PROPN ejpam-3086 118 9 and and CCONJ ejpam-3086 118 10 m m NOUN ejpam-3086 118 11 ´ ´ NOUN ejpam-3086 118 12 is be AUX ejpam-3086 118 13 called call VERB ejpam-3086 118 14 a a DET ejpam-3086 118 15 harmonic harmonic ADJ ejpam-3086 118 16 map map NOUN ejpam-3086 118 17 if if SCONJ ejpam-3086 118 18 τ(f τ(f NOUN ejpam-3086 118 19 ) ) PUNCT ejpam-3086 118 20 = = SYM ejpam-3086 119 1 0 0 X ejpam-3086 119 2 . . PUNCT ejpam-3086 119 3 definition definition NOUN ejpam-3086 119 4 2 2 NUM ejpam-3086 119 5 . . PUNCT ejpam-3086 120 1 ( ( PUNCT ejpam-3086 120 2 [ [ X ejpam-3086 120 3 8 8 NUM ejpam-3086 120 4 ] ] PUNCT ejpam-3086 120 5 ) ) PUNCT ejpam-3086 120 6 let let VERB ejpam-3086 120 7 m m VERB ejpam-3086 120 8 = = SYM ejpam-3086 120 9 ( ( PUNCT ejpam-3086 120 10 m m PROPN ejpam-3086 120 11 , , PUNCT ejpam-3086 120 12 φ φ PROPN ejpam-3086 120 13 , , PUNCT ejpam-3086 120 14 ξ ξ PROPN ejpam-3086 120 15 , , PUNCT ejpam-3086 120 16 η η NOUN ejpam-3086 120 17 , , PUNCT ejpam-3086 120 18 g g NOUN ejpam-3086 120 19 ) ) PUNCT ejpam-3086 120 20 and and CCONJ ejpam-3086 120 21 m´= m´= NOUN ejpam-3086 120 22 ( ( PUNCT ejpam-3086 120 23 m,́ m,́ PROPN ejpam-3086 120 24 φ́ φ́ PROPN ejpam-3086 120 25 , , PUNCT ejpam-3086 120 26 ξ́ ξ́ PROPN ejpam-3086 120 27 , , PUNCT ejpam-3086 120 28 ή ή PROPN ejpam-3086 120 29 , , PUNCT ejpam-3086 120 30 ǵ ǵ NOUN ejpam-3086 120 31 ) ) PUNCT ejpam-3086 120 32 be be VERB ejpam-3086 120 33 two two NUM ejpam-3086 120 34 almost almost ADV ejpam-3086 120 35 contact contact NOUN ejpam-3086 120 36 metric metric ADJ ejpam-3086 120 37 manifolds manifold NOUN ejpam-3086 120 38 . . PUNCT ejpam-3086 121 1 we we PRON ejpam-3086 121 2 say say VERB ejpam-3086 121 3 that that SCONJ ejpam-3086 121 4 a a DET ejpam-3086 121 5 differentiable differentiable ADJ ejpam-3086 121 6 map map NOUN ejpam-3086 121 7 f f X ejpam-3086 121 8 : : PUNCT ejpam-3086 121 9 m m PROPN ejpam-3086 121 10 → → SYM ejpam-3086 121 11 m m PRON ejpam-3086 121 12 ´ ´ NOUN ejpam-3086 121 13 is be AUX ejpam-3086 121 14 ( ( PUNCT ejpam-3086 121 15 φ φ NOUN ejpam-3086 121 16 , , PUNCT ejpam-3086 121 17 φ́)-holomorphic φ́)-holomorphic ADJ ejpam-3086 121 18 if if SCONJ ejpam-3086 121 19 dfoφ dfoφ ADJ ejpam-3086 121 20 = = SYM ejpam-3086 121 21 φ́odf φ́odf X ejpam-3086 121 22 and and CCONJ ejpam-3086 121 23 f f PROPN ejpam-3086 121 24 is be AUX ejpam-3086 121 25 ( ( PUNCT ejpam-3086 121 26 φ φ NOUN ejpam-3086 121 27 , , PUNCT ejpam-3086 121 28 φ́)-antiholomorphic φ́)-antiholomorphic ADJ ejpam-3086 121 29 if if SCONJ ejpam-3086 121 30 dfoφ dfoφ ADJ ejpam-3086 121 31 = = SYM ejpam-3086 121 32 −φ́odf −φ́odf NOUN ejpam-3086 121 33 . . PUNCT ejpam-3086 122 1 f. f. PROPN ejpam-3086 122 2 malek malek PROPN ejpam-3086 122 3 , , PUNCT ejpam-3086 122 4 m. m. NOUN ejpam-3086 122 5 samanipour samanipour PROPN ejpam-3086 122 6 / / SYM ejpam-3086 122 7 eur eur PROPN ejpam-3086 122 8 . . PUNCT ejpam-3086 123 1 j. j. PROPN ejpam-3086 123 2 pure pure PROPN ejpam-3086 123 3 appl appl PROPN ejpam-3086 123 4 . . PROPN ejpam-3086 123 5 math math PROPN ejpam-3086 123 6 , , PUNCT ejpam-3086 123 7 10 10 NUM ejpam-3086 123 8 ( ( PUNCT ejpam-3086 123 9 5 5 NUM ejpam-3086 123 10 ) ) PUNCT ejpam-3086 123 11 ( ( PUNCT ejpam-3086 123 12 2017 2017 NUM ejpam-3086 123 13 ) ) PUNCT ejpam-3086 123 14 , , PUNCT ejpam-3086 123 15 946 946 NUM ejpam-3086 123 16 - - SYM ejpam-3086 123 17 954 954 NUM ejpam-3086 123 18 951 951 NUM ejpam-3086 123 19 proposition proposition NOUN ejpam-3086 123 20 1 1 NUM ejpam-3086 123 21 . . PUNCT ejpam-3086 124 1 let let VERB ejpam-3086 124 2 m m VERB ejpam-3086 124 3 = = SYM ejpam-3086 124 4 ( ( PUNCT ejpam-3086 124 5 m m PROPN ejpam-3086 124 6 , , PUNCT ejpam-3086 124 7 φ φ PROPN ejpam-3086 124 8 , , PUNCT ejpam-3086 124 9 ξ ξ PROPN ejpam-3086 124 10 , , PUNCT ejpam-3086 124 11 η η NOUN ejpam-3086 124 12 , , PUNCT ejpam-3086 124 13 g g NOUN ejpam-3086 124 14 ) ) PUNCT ejpam-3086 124 15 be be VERB ejpam-3086 124 16 a a DET ejpam-3086 124 17 quasi quasi ADJ ejpam-3086 124 18 contact contact NOUN ejpam-3086 124 19 metric metric NOUN ejpam-3086 124 20 ( ( PUNCT ejpam-3086 124 21 or or CCONJ ejpam-3086 124 22 nearly nearly ADV ejpam-3086 124 23 sasakain sasakain NOUN ejpam-3086 124 24 ) ) PUNCT ejpam-3086 124 25 manifold manifold ADJ ejpam-3086 124 26 . . PUNCT ejpam-3086 125 1 if if SCONJ ejpam-3086 125 2 a a DET ejpam-3086 125 3 transformation transformation NOUN ejpam-3086 125 4 µ µ X ejpam-3086 125 5 on on ADP ejpam-3086 125 6 m m PROPN ejpam-3086 125 7 leaves leave NOUN ejpam-3086 125 8 φ φ PROPN ejpam-3086 125 9 invariant invariant PROPN ejpam-3086 125 10 that that PRON ejpam-3086 125 11 means mean VERB ejpam-3086 125 12 φµ φµ X ejpam-3086 125 13 = = VERB ejpam-3086 125 14 µφ µφ PROPN ejpam-3086 125 15 , , PUNCT ejpam-3086 125 16 then then ADV ejpam-3086 125 17 there there PRON ejpam-3086 125 18 exists exist VERB ejpam-3086 125 19 α α PRON ejpam-3086 125 20 ∈ ∈ NOUN ejpam-3086 125 21 r r NOUN ejpam-3086 125 22 such such ADJ ejpam-3086 125 23 that that SCONJ ejpam-3086 125 24 the the DET ejpam-3086 125 25 following follow VERB ejpam-3086 125 26 relations relation NOUN ejpam-3086 125 27 are be AUX ejpam-3086 125 28 hold hold ADJ ejpam-3086 125 29 : : PUNCT ejpam-3086 125 30 ( ( PUNCT ejpam-3086 125 31 a a X ejpam-3086 125 32 ) ) PUNCT ejpam-3086 125 33 µ∗η µ∗η X ejpam-3086 125 34 = = SYM ejpam-3086 125 35 αη αη PROPN ejpam-3086 125 36 ( ( PUNCT ejpam-3086 125 37 b b NOUN ejpam-3086 125 38 ) ) PUNCT ejpam-3086 125 39 µξ µξ ADP ejpam-3086 125 40 = = SYM ejpam-3086 125 41 αξ αξ PROPN ejpam-3086 125 42 ( ( PUNCT ejpam-3086 125 43 c c NOUN ejpam-3086 125 44 ) ) PUNCT ejpam-3086 125 45 µ∗φ µ∗φ PROPN ejpam-3086 125 46 = = SYM ejpam-3086 125 47 αφ αφ PROPN ejpam-3086 125 48 proof proof NOUN ejpam-3086 125 49 . . PUNCT ejpam-3086 126 1 first first ADV ejpam-3086 126 2 we we PRON ejpam-3086 126 3 prove prove VERB ejpam-3086 126 4 ( ( PUNCT ejpam-3086 126 5 a a X ejpam-3086 126 6 ) ) PUNCT ejpam-3086 126 7 and and CCONJ ejpam-3086 126 8 ( ( PUNCT ejpam-3086 126 9 b b NOUN ejpam-3086 126 10 ) ) PUNCT ejpam-3086 126 11 for for ADP ejpam-3086 126 12 some some DET ejpam-3086 126 13 α α PRON ejpam-3086 126 14 ∈ ∈ NOUN ejpam-3086 126 15 c∞(m c∞(m NOUN ejpam-3086 126 16 ) ) PUNCT ejpam-3086 126 17 , , PUNCT ejpam-3086 126 18 then then ADV ejpam-3086 126 19 we we PRON ejpam-3086 126 20 prove prove VERB ejpam-3086 126 21 that that SCONJ ejpam-3086 126 22 α α PRON ejpam-3086 126 23 must must AUX ejpam-3086 126 24 be be AUX ejpam-3086 126 25 constant constant ADJ ejpam-3086 126 26 . . PUNCT ejpam-3086 127 1 ( ( PUNCT ejpam-3086 127 2 a a X ejpam-3086 127 3 ) ) PUNCT ejpam-3086 127 4 from from ADP ejpam-3086 127 5 ηoφ ηoφ VERB ejpam-3086 127 6 = = SYM ejpam-3086 127 7 0 0 PUNCT ejpam-3086 127 8 and and CCONJ ejpam-3086 127 9 φµ φµ X ejpam-3086 127 10 = = SYM ejpam-3086 127 11 µφ µφ PROPN ejpam-3086 127 12 , , PUNCT ejpam-3086 127 13 we we PRON ejpam-3086 127 14 have have VERB ejpam-3086 127 15 ηoµφ ηoµφ NOUN ejpam-3086 127 16 = = SYM ejpam-3086 127 17 0 0 NUM ejpam-3086 127 18 . . PUNCT ejpam-3086 128 1 thus thus ADV ejpam-3086 128 2 at at ADP ejpam-3086 128 3 any any DET ejpam-3086 128 4 point point NOUN ejpam-3086 128 5 x x PUNCT ejpam-3086 128 6 of of ADP ejpam-3086 128 7 m m VERB ejpam-3086 128 8 we we PRON ejpam-3086 128 9 have have VERB ejpam-3086 128 10 : : PUNCT ejpam-3086 128 11 ( ( PUNCT ejpam-3086 128 12 µ∗η)(φx)x µ∗η)(φx)x PROPN ejpam-3086 128 13 = = NOUN ejpam-3086 128 14 0 0 NUM ejpam-3086 128 15 , , PUNCT ejpam-3086 128 16 x x X ejpam-3086 128 17 ∈ ∈ PROPN ejpam-3086 128 18 χ(m χ(m PROPN ejpam-3086 128 19 ) ) PUNCT ejpam-3086 128 20 . . PUNCT ejpam-3086 129 1 so so ADV ejpam-3086 129 2 , , PUNCT ejpam-3086 129 3 ( ( PUNCT ejpam-3086 129 4 µ∗η)x µ∗η)x ADP ejpam-3086 129 5 = = NOUN ejpam-3086 129 6 α(x)ηx α(x)ηx NOUN ejpam-3086 129 7 , , PUNCT ejpam-3086 129 8 for for ADP ejpam-3086 129 9 some some DET ejpam-3086 129 10 α α PRON ejpam-3086 129 11 ∈ ∈ NOUN ejpam-3086 129 12 c∞(m c∞(m NOUN ejpam-3086 129 13 ) ) PUNCT ejpam-3086 129 14 . . PUNCT ejpam-3086 130 1 ( ( PUNCT ejpam-3086 130 2 b b X ejpam-3086 130 3 ) ) PUNCT ejpam-3086 130 4 from from ADP ejpam-3086 130 5 φξ φξ NOUN ejpam-3086 130 6 = = SYM ejpam-3086 130 7 0 0 NUM ejpam-3086 130 8 and and CCONJ ejpam-3086 130 9 φµ φµ X ejpam-3086 130 10 = = SYM ejpam-3086 130 11 µφ µφ PROPN ejpam-3086 130 12 , , PUNCT ejpam-3086 130 13 we we PRON ejpam-3086 130 14 have have VERB ejpam-3086 130 15 φµξ φµξ NOUN ejpam-3086 130 16 = = SYM ejpam-3086 130 17 0 0 X ejpam-3086 130 18 . . PUNCT ejpam-3086 131 1 so so ADV ejpam-3086 131 2 , , PUNCT ejpam-3086 131 3 µξ µξ ADV ejpam-3086 131 4 = = SYM ejpam-3086 131 5 βξ βξ NOUN ejpam-3086 131 6 , , PUNCT ejpam-3086 131 7 for for ADP ejpam-3086 131 8 some some DET ejpam-3086 131 9 β β X ejpam-3086 131 10 ∈ ∈ PROPN ejpam-3086 131 11 c∞(m c∞(m NOUN ejpam-3086 131 12 ) ) PUNCT ejpam-3086 131 13 . . PUNCT ejpam-3086 132 1 therefore therefore ADV ejpam-3086 132 2 η(µξ η(µξ ADV ejpam-3086 132 3 ) ) PUNCT ejpam-3086 132 4 = = SYM ejpam-3086 133 1 η(βξ η(βξ X ejpam-3086 133 2 ) ) PUNCT ejpam-3086 133 3 and and CCONJ ejpam-3086 133 4 then then ADV ejpam-3086 133 5 ( ( PUNCT ejpam-3086 133 6 µ∗η)ξ µ∗η)ξ X ejpam-3086 133 7 = = PUNCT ejpam-3086 133 8 βη(ξ βη(ξ PUNCT ejpam-3086 133 9 ) ) PUNCT ejpam-3086 133 10 . . PUNCT ejpam-3086 134 1 by by ADP ejpam-3086 134 2 ( ( PUNCT ejpam-3086 134 3 a a X ejpam-3086 134 4 ) ) PUNCT ejpam-3086 134 5 it it PRON ejpam-3086 134 6 follows follow VERB ejpam-3086 134 7 that that SCONJ ejpam-3086 134 8 α α PROPN ejpam-3086 134 9 = = SYM ejpam-3086 134 10 β β X ejpam-3086 134 11 . . PUNCT ejpam-3086 135 1 now now ADV ejpam-3086 135 2 , , PUNCT ejpam-3086 135 3 we we PRON ejpam-3086 135 4 show show VERB ejpam-3086 135 5 that that SCONJ ejpam-3086 135 6 α α PRON ejpam-3086 135 7 must must AUX ejpam-3086 135 8 be be AUX ejpam-3086 135 9 constant constant ADJ ejpam-3086 135 10 . . PUNCT ejpam-3086 136 1 by by ADP ejpam-3086 136 2 differentiation differentiation NOUN ejpam-3086 136 3 ( ( PUNCT ejpam-3086 136 4 a a X ejpam-3086 136 5 ) ) PUNCT ejpam-3086 136 6 , , PUNCT ejpam-3086 136 7 we we PRON ejpam-3086 136 8 get get VERB ejpam-3086 136 9 : : PUNCT ejpam-3086 136 10 dµ∗η dµ∗η PROPN ejpam-3086 136 11 = = PUNCT ejpam-3086 136 12 dα dα PRON ejpam-3086 136 13 ∧ ∧ PROPN ejpam-3086 136 14 η η PROPN ejpam-3086 136 15 + + PROPN ejpam-3086 136 16 αdη αdη X ejpam-3086 136 17 . . PUNCT ejpam-3086 137 1 ( ( PUNCT ejpam-3086 137 2 4 4 NUM ejpam-3086 137 3 ) ) PUNCT ejpam-3086 137 4 since since SCONJ ejpam-3086 137 5 d d PROPN ejpam-3086 137 6 and and CCONJ ejpam-3086 137 7 µ∗ µ∗ VERB ejpam-3086 137 8 commute commute NOUN ejpam-3086 137 9 and and CCONJ ejpam-3086 137 10 by by ADP ejpam-3086 137 11 corollary corollary ADJ ejpam-3086 137 12 1 1 NUM ejpam-3086 137 13 and and CCONJ ejpam-3086 137 14 ( ( PUNCT ejpam-3086 137 15 4 4 NUM ejpam-3086 137 16 ) ) PUNCT ejpam-3086 137 17 , , PUNCT ejpam-3086 137 18 we we PRON ejpam-3086 137 19 have have VERB ejpam-3086 137 20 : : PUNCT ejpam-3086 137 21 0 0 NUM ejpam-3086 137 22 = = SYM ejpam-3086 137 23 dη(αξ dη(αξ PROPN ejpam-3086 137 24 , , PUNCT ejpam-3086 137 25 µξ µξ ADP ejpam-3086 137 26 ) ) PUNCT ejpam-3086 137 27 = = SYM ejpam-3086 137 28 dη(µξ dη(µξ PROPN ejpam-3086 137 29 , , PUNCT ejpam-3086 137 30 µy µy X ejpam-3086 137 31 ) ) PUNCT ejpam-3086 138 1 = = SYM ejpam-3086 138 2 µ∗dη(ξ µ∗dη(ξ ADJ ejpam-3086 138 3 , , PUNCT ejpam-3086 138 4 y y PROPN ejpam-3086 138 5 ) ) PUNCT ejpam-3086 138 6 = = PUNCT ejpam-3086 139 1 dµ∗η(ξ dµ∗η(ξ PROPN ejpam-3086 139 2 , , PUNCT ejpam-3086 139 3 y y PROPN ejpam-3086 139 4 ) ) PUNCT ejpam-3086 140 1 = = PRON ejpam-3086 140 2 dα dα PRON ejpam-3086 140 3 ∧ ∧ PROPN ejpam-3086 140 4 η(ξ η(ξ PROPN ejpam-3086 140 5 , , PUNCT ejpam-3086 140 6 y y PROPN ejpam-3086 140 7 ) ) PUNCT ejpam-3086 141 1 + + PUNCT ejpam-3086 141 2 αdη(ξ αdη(ξ PROPN ejpam-3086 141 3 , , PUNCT ejpam-3086 141 4 y y NOUN ejpam-3086 141 5 ) ) PUNCT ejpam-3086 142 1 = = SYM ejpam-3086 142 2 dα(ξ)η(y dα(ξ)η(y PROPN ejpam-3086 142 3 ) ) PUNCT ejpam-3086 143 1 − − NOUN ejpam-3086 143 2 dα(y dα(y NOUN ejpam-3086 143 3 ) ) PUNCT ejpam-3086 143 4 , , PUNCT ejpam-3086 143 5 y y PROPN ejpam-3086 143 6 ∈ ∈ PROPN ejpam-3086 143 7 χ(m χ(m PROPN ejpam-3086 143 8 ) ) PUNCT ejpam-3086 143 9 . . PUNCT ejpam-3086 144 1 so so ADV ejpam-3086 144 2 , , PUNCT ejpam-3086 144 3 dα(ξ)η dα(ξ)η PROPN ejpam-3086 144 4 = = SYM ejpam-3086 144 5 dα dα PROPN ejpam-3086 144 6 . . PUNCT ejpam-3086 145 1 ( ( PUNCT ejpam-3086 145 2 5 5 NUM ejpam-3086 145 3 ) ) PUNCT ejpam-3086 145 4 therefore therefore ADV ejpam-3086 145 5 , , PUNCT ejpam-3086 145 6 dα(ξ)η∧η dα(ξ)η∧η PUNCT ejpam-3086 145 7 = = SYM ejpam-3086 145 8 dα∧η dα∧η PROPN ejpam-3086 145 9 . . PUNCT ejpam-3086 146 1 then then ADV ejpam-3086 146 2 , , PUNCT ejpam-3086 146 3 we we PRON ejpam-3086 146 4 have have VERB ejpam-3086 146 5 dα∧η dα∧η NOUN ejpam-3086 146 6 = = SYM ejpam-3086 146 7 0 0 NUM ejpam-3086 146 8 , , PUNCT ejpam-3086 146 9 and and CCONJ ejpam-3086 146 10 by by ADP ejpam-3086 146 11 differentation differentation NOUN ejpam-3086 146 12 , , PUNCT ejpam-3086 146 13 we we PRON ejpam-3086 146 14 obtain obtain VERB ejpam-3086 146 15 dα∧ dα∧ PROPN ejpam-3086 146 16 dη dη NOUN ejpam-3086 146 17 = = NOUN ejpam-3086 146 18 0 0 PROPN ejpam-3086 146 19 . . PUNCT ejpam-3086 147 1 so so ADV ejpam-3086 147 2 ( ( PUNCT ejpam-3086 147 3 5 5 NUM ejpam-3086 147 4 ) ) PUNCT ejpam-3086 147 5 implies imply VERB ejpam-3086 147 6 dα(ξ)η dα(ξ)η X ejpam-3086 147 7 ∧ ∧ NOUN ejpam-3086 147 8 dη dη NOUN ejpam-3086 147 9 = = NOUN ejpam-3086 147 10 0 0 NUM ejpam-3086 147 11 and and CCONJ ejpam-3086 147 12 by by ADP ejpam-3086 147 13 theorem theorem NOUN ejpam-3086 147 14 3 3 NUM ejpam-3086 147 15 , , PUNCT ejpam-3086 147 16 it it PRON ejpam-3086 147 17 follows follow VERB ejpam-3086 147 18 that that PRON ejpam-3086 147 19 dα(ξ dα(ξ X ejpam-3086 147 20 ) ) PUNCT ejpam-3086 147 21 = = SYM ejpam-3086 148 1 0 0 X ejpam-3086 148 2 . . PUNCT ejpam-3086 148 3 again again ADV ejpam-3086 148 4 , , PUNCT ejpam-3086 148 5 condition condition NOUN ejpam-3086 148 6 ( ( PUNCT ejpam-3086 148 7 5 5 NUM ejpam-3086 148 8 ) ) PUNCT ejpam-3086 148 9 gives give VERB ejpam-3086 148 10 dα dα NOUN ejpam-3086 148 11 = = SYM ejpam-3086 148 12 0 0 NUM ejpam-3086 148 13 , , PUNCT ejpam-3086 148 14 i.e i.e PRON ejpam-3086 148 15 , , PUNCT ejpam-3086 148 16 α α PROPN ejpam-3086 148 17 is be AUX ejpam-3086 148 18 constant constant ADJ ejpam-3086 148 19 . . PUNCT ejpam-3086 149 1 f. f. PROPN ejpam-3086 149 2 malek malek PROPN ejpam-3086 149 3 , , PUNCT ejpam-3086 149 4 m. m. NOUN ejpam-3086 149 5 samanipour samanipour PROPN ejpam-3086 149 6 / / SYM ejpam-3086 149 7 eur eur PROPN ejpam-3086 149 8 . . PUNCT ejpam-3086 150 1 j. j. PROPN ejpam-3086 150 2 pure pure PROPN ejpam-3086 150 3 appl appl PROPN ejpam-3086 150 4 . . PROPN ejpam-3086 150 5 math math PROPN ejpam-3086 150 6 , , PUNCT ejpam-3086 150 7 10 10 NUM ejpam-3086 150 8 ( ( PUNCT ejpam-3086 150 9 5 5 NUM ejpam-3086 150 10 ) ) PUNCT ejpam-3086 150 11 ( ( PUNCT ejpam-3086 150 12 2017 2017 NUM ejpam-3086 150 13 ) ) PUNCT ejpam-3086 150 14 , , PUNCT ejpam-3086 150 15 946 946 NUM ejpam-3086 150 16 - - SYM ejpam-3086 150 17 954 954 NUM ejpam-3086 150 18 952 952 NUM ejpam-3086 150 19 ( ( PUNCT ejpam-3086 150 20 c c NOUN ejpam-3086 150 21 ) ) PUNCT ejpam-3086 150 22 now now ADV ejpam-3086 150 23 by by ADP ejpam-3086 150 24 ( ( PUNCT ejpam-3086 150 25 4 4 NUM ejpam-3086 150 26 ) ) PUNCT ejpam-3086 150 27 , , PUNCT ejpam-3086 150 28 it it PRON ejpam-3086 150 29 follows follow VERB ejpam-3086 150 30 that that SCONJ ejpam-3086 150 31 µ∗dη µ∗dη PROPN ejpam-3086 150 32 = = SYM ejpam-3086 150 33 αdη αdη NOUN ejpam-3086 150 34 . . PUNCT ejpam-3086 151 1 by by ADP ejpam-3086 151 2 lemma lemma PROPN ejpam-3086 151 3 2 2 NUM ejpam-3086 151 4 ( ( PUNCT ejpam-3086 151 5 2φ 2φ NUM ejpam-3086 151 6 = = SYM ejpam-3086 151 7 dη dη NOUN ejpam-3086 152 1 + + CCONJ ejpam-3086 152 2 dη dη NOUN ejpam-3086 152 3 o o PROPN ejpam-3086 152 4 φ φ PROPN ejpam-3086 152 5 ⊗ ⊗ PROPN ejpam-3086 152 6 φ φ PROPN ejpam-3086 152 7 ) ) PUNCT ejpam-3086 152 8 we we PRON ejpam-3086 152 9 have have VERB ejpam-3086 152 10 : : PUNCT ejpam-3086 152 11 ( ( PUNCT ejpam-3086 152 12 µ∗φ µ∗φ NOUN ejpam-3086 152 13 ) ) PUNCT ejpam-3086 152 14 = = SYM ejpam-3086 152 15 1 1 NUM ejpam-3086 152 16 2 2 NUM ejpam-3086 152 17 ( ( PUNCT ejpam-3086 152 18 µ∗dη µ∗dη NOUN ejpam-3086 152 19 + + CCONJ ejpam-3086 152 20 µ∗dη µ∗dη PROPN ejpam-3086 152 21 o o PROPN ejpam-3086 152 22 φ⊗ φ⊗ NOUN ejpam-3086 152 23 φ φ NOUN ejpam-3086 152 24 ) ) PUNCT ejpam-3086 152 25 = = SYM ejpam-3086 153 1 α α X ejpam-3086 153 2 2 2 NUM ejpam-3086 153 3 ( ( PUNCT ejpam-3086 153 4 dη dη NOUN ejpam-3086 154 1 + + CCONJ ejpam-3086 154 2 dη dη NOUN ejpam-3086 154 3 o o PROPN ejpam-3086 154 4 φ⊗ φ⊗ PROPN ejpam-3086 154 5 φ φ PROPN ejpam-3086 154 6 ) ) PUNCT ejpam-3086 154 7 = = SYM ejpam-3086 154 8 αφ αφ X ejpam-3086 154 9 . . PUNCT ejpam-3086 155 1 in in ADP ejpam-3086 155 2 ( ( PUNCT ejpam-3086 155 3 [ [ X ejpam-3086 155 4 6 6 NUM ejpam-3086 155 5 ] ] NUM ejpam-3086 155 6 ) ) PUNCT ejpam-3086 155 7 , , PUNCT ejpam-3086 155 8 tanno tanno PROPN ejpam-3086 155 9 studied study VERB ejpam-3086 155 10 conformal conformal ADJ ejpam-3086 155 11 transformation transformation NOUN ejpam-3086 155 12 on on ADP ejpam-3086 155 13 contact contact NOUN ejpam-3086 155 14 metric metric ADJ ejpam-3086 155 15 manifold manifold NOUN ejpam-3086 155 16 . . PUNCT ejpam-3086 156 1 in in ADP ejpam-3086 156 2 the the DET ejpam-3086 156 3 following following NOUN ejpam-3086 156 4 theorem theorem NOUN ejpam-3086 156 5 , , PUNCT ejpam-3086 156 6 the the DET ejpam-3086 156 7 same same ADJ ejpam-3086 156 8 result result NOUN ejpam-3086 156 9 is be AUX ejpam-3086 156 10 proved prove VERB ejpam-3086 156 11 for for ADP ejpam-3086 156 12 quasi quasi ADJ ejpam-3086 156 13 contact contact NOUN ejpam-3086 156 14 metric metric ADJ ejpam-3086 156 15 and and CCONJ ejpam-3086 156 16 nearly nearly ADV ejpam-3086 156 17 sasakain sasakain NOUN ejpam-3086 156 18 manifolds manifold NOUN ejpam-3086 156 19 . . PUNCT ejpam-3086 157 1 theorem theorem NOUN ejpam-3086 157 2 4 4 NUM ejpam-3086 157 3 . . PUNCT ejpam-3086 158 1 let let VERB ejpam-3086 158 2 m m VERB ejpam-3086 158 3 = = SYM ejpam-3086 158 4 ( ( PUNCT ejpam-3086 158 5 m m PROPN ejpam-3086 158 6 , , PUNCT ejpam-3086 158 7 φ φ PROPN ejpam-3086 158 8 , , PUNCT ejpam-3086 158 9 ξ ξ PROPN ejpam-3086 158 10 , , PUNCT ejpam-3086 158 11 η η NOUN ejpam-3086 158 12 , , PUNCT ejpam-3086 158 13 g g NOUN ejpam-3086 158 14 ) ) PUNCT ejpam-3086 158 15 be be VERB ejpam-3086 158 16 a a DET ejpam-3086 158 17 quasi quasi ADJ ejpam-3086 158 18 contact contact NOUN ejpam-3086 158 19 metric metric NOUN ejpam-3086 158 20 ( ( PUNCT ejpam-3086 158 21 or or CCONJ ejpam-3086 158 22 nearly nearly ADV ejpam-3086 158 23 sasakain sasakain NOUN ejpam-3086 158 24 ) ) PUNCT ejpam-3086 158 25 manifold manifold ADJ ejpam-3086 158 26 . . PUNCT ejpam-3086 159 1 if if SCONJ ejpam-3086 159 2 a a DET ejpam-3086 159 3 transformation transformation NOUN ejpam-3086 159 4 µ µ X ejpam-3086 159 5 on on ADP ejpam-3086 159 6 m m PROPN ejpam-3086 159 7 leaves leave NOUN ejpam-3086 159 8 φ φ PROPN ejpam-3086 159 9 invariant invariant PROPN ejpam-3086 159 10 , , PUNCT ejpam-3086 159 11 then then ADV ejpam-3086 159 12 µ µ NOUN ejpam-3086 159 13 is be AUX ejpam-3086 159 14 a a DET ejpam-3086 159 15 homothety homothety NOUN ejpam-3086 159 16 ( ( PUNCT ejpam-3086 159 17 that that PRON ejpam-3086 159 18 means mean VERB ejpam-3086 159 19 µ∗g µ∗g NUM ejpam-3086 159 20 = = PUNCT ejpam-3086 159 21 c2 c2 PROPN ejpam-3086 159 22 g g PROPN ejpam-3086 159 23 for for ADP ejpam-3086 159 24 some some DET ejpam-3086 159 25 nonzero nonzero NOUN ejpam-3086 159 26 scalar scalar ADJ ejpam-3086 159 27 c c PROPN ejpam-3086 159 28 ) ) PUNCT ejpam-3086 159 29 on on ADP ejpam-3086 159 30 γ(d γ(d NOUN ejpam-3086 159 31 ) ) PUNCT ejpam-3086 159 32 in in ADP ejpam-3086 159 33 which which PRON ejpam-3086 159 34 d d NOUN ejpam-3086 159 35 = = PRON ejpam-3086 159 36 { { PUNCT ejpam-3086 159 37 x x PROPN ejpam-3086 159 38 ∈ ∈ PROPN ejpam-3086 159 39 tm tm NOUN ejpam-3086 159 40 ; ; PUNCT ejpam-3086 159 41 η(x η(x X ejpam-3086 159 42 ) ) PUNCT ejpam-3086 159 43 = = SYM ejpam-3086 159 44 0 0 NUM ejpam-3086 159 45 } } PUNCT ejpam-3086 159 46 ) ) PUNCT ejpam-3086 159 47 . . PUNCT ejpam-3086 160 1 proof proof NOUN ejpam-3086 160 2 . . PUNCT ejpam-3086 161 1 for for ADP ejpam-3086 161 2 an an DET ejpam-3086 161 3 arbitrary arbitrary ADJ ejpam-3086 161 4 x x SYM ejpam-3086 161 5 ∈m ∈m NOUN ejpam-3086 161 6 and and CCONJ ejpam-3086 161 7 x x NOUN ejpam-3086 161 8 , , PUNCT ejpam-3086 161 9 y y PROPN ejpam-3086 161 10 ∈ ∈ PROPN ejpam-3086 161 11 γ(d γ(d PROPN ejpam-3086 161 12 ) ) PUNCT ejpam-3086 161 13 . . PUNCT ejpam-3086 162 1 we we PRON ejpam-3086 162 2 have have VERB ejpam-3086 162 3 : : PUNCT ejpam-3086 162 4 ( ( PUNCT ejpam-3086 162 5 µ∗φ)x(x µ∗φ)x(x ADP ejpam-3086 162 6 , , PUNCT ejpam-3086 162 7 y y NOUN ejpam-3086 162 8 ) ) PUNCT ejpam-3086 162 9 = = SYM ejpam-3086 162 10 φ(µx φ(µx PROPN ejpam-3086 162 11 , , PUNCT ejpam-3086 162 12 µy µy ADV ejpam-3086 162 13 ) ) PUNCT ejpam-3086 162 14 . . PUNCT ejpam-3086 163 1 so so ADV ejpam-3086 163 2 , , PUNCT ejpam-3086 163 3 αφx(x αφx(x PROPN ejpam-3086 163 4 , , PUNCT ejpam-3086 163 5 y y NOUN ejpam-3086 163 6 ) ) PUNCT ejpam-3086 163 7 = = SYM ejpam-3086 163 8 g(µx g(µx PROPN ejpam-3086 163 9 , , PUNCT ejpam-3086 163 10 µφy µφy NOUN ejpam-3086 163 11 ) ) PUNCT ejpam-3086 163 12 = = SYM ejpam-3086 163 13 ( ( PUNCT ejpam-3086 163 14 µ∗g)x(x µ∗g)x(x ADP ejpam-3086 163 15 , , PUNCT ejpam-3086 163 16 φy φy NOUN ejpam-3086 163 17 ) ) PUNCT ejpam-3086 163 18 . . PUNCT ejpam-3086 164 1 thus thus ADV ejpam-3086 164 2 we we PRON ejpam-3086 164 3 have have VERB ejpam-3086 164 4 αgx(x αgx(x NUM ejpam-3086 164 5 , , PUNCT ejpam-3086 164 6 φy φy NOUN ejpam-3086 164 7 ) ) PUNCT ejpam-3086 164 8 = = SYM ejpam-3086 164 9 ( ( PUNCT ejpam-3086 164 10 µ∗g)x(x µ∗g)x(x ADP ejpam-3086 164 11 , , PUNCT ejpam-3086 164 12 φy φy NOUN ejpam-3086 164 13 ) ) PUNCT ejpam-3086 164 14 . . PUNCT ejpam-3086 165 1 substituting substitute VERB ejpam-3086 165 2 y y PROPN ejpam-3086 165 3 by by ADP ejpam-3086 165 4 −φx −φx PROPN ejpam-3086 165 5 and and CCONJ ejpam-3086 165 6 we we PRON ejpam-3086 165 7 get get VERB ejpam-3086 165 8 ( ( PUNCT ejpam-3086 165 9 µ∗g)(x µ∗g)(x NOUN ejpam-3086 165 10 , , PUNCT ejpam-3086 165 11 x x NOUN ejpam-3086 165 12 ) ) PUNCT ejpam-3086 165 13 = = SYM ejpam-3086 165 14 αg(x αg(x X ejpam-3086 165 15 , , PUNCT ejpam-3086 165 16 x x NOUN ejpam-3086 165 17 ) ) PUNCT ejpam-3086 165 18 , , PUNCT ejpam-3086 165 19 then then ADV ejpam-3086 165 20 α α X ejpam-3086 165 21 > > X ejpam-3086 165 22 0 0 PROPN ejpam-3086 165 23 . . PUNCT ejpam-3086 165 24 theorem theorem NOUN ejpam-3086 165 25 5 5 NUM ejpam-3086 165 26 . . PUNCT ejpam-3086 166 1 let let AUX ejpam-3086 166 2 m m VERB ejpam-3086 166 3 = = SYM ejpam-3086 166 4 ( ( PUNCT ejpam-3086 166 5 m m PROPN ejpam-3086 166 6 , , PUNCT ejpam-3086 166 7 φ φ PROPN ejpam-3086 166 8 , , PUNCT ejpam-3086 166 9 ξ ξ PROPN ejpam-3086 166 10 , , PUNCT ejpam-3086 166 11 η η NOUN ejpam-3086 166 12 , , PUNCT ejpam-3086 166 13 g g NOUN ejpam-3086 166 14 ) ) PUNCT ejpam-3086 166 15 and and CCONJ ejpam-3086 166 16 m´= m´= NOUN ejpam-3086 166 17 ( ( PUNCT ejpam-3086 166 18 m,́ m,́ PROPN ejpam-3086 166 19 φ́ φ́ PROPN ejpam-3086 166 20 , , PUNCT ejpam-3086 166 21 ξ́ ξ́ PROPN ejpam-3086 166 22 , , PUNCT ejpam-3086 166 23 ή ή PROPN ejpam-3086 166 24 , , PUNCT ejpam-3086 166 25 ǵ ǵ NOUN ejpam-3086 166 26 ) ) PUNCT ejpam-3086 166 27 be be VERB ejpam-3086 166 28 two two NUM ejpam-3086 166 29 quasi quasi ADJ ejpam-3086 166 30 contact contact NOUN ejpam-3086 166 31 metric metric ADJ ejpam-3086 166 32 manifolds manifold NOUN ejpam-3086 166 33 . . PUNCT ejpam-3086 167 1 any any DET ejpam-3086 167 2 ( ( PUNCT ejpam-3086 167 3 φ φ PROPN ejpam-3086 167 4 , , PUNCT ejpam-3086 167 5 φ́)-holomorphic φ́)-holomorphic PROPN ejpam-3086 167 6 ( ( PUNCT ejpam-3086 167 7 or or CCONJ ejpam-3086 167 8 ( ( PUNCT ejpam-3086 167 9 φ φ NOUN ejpam-3086 167 10 , , PUNCT ejpam-3086 167 11 φ́)-antiholomorphic φ́)-antiholomorphic ADJ ejpam-3086 167 12 ) ) PUNCT ejpam-3086 167 13 submersion submersion NOUN ejpam-3086 167 14 f f NOUN ejpam-3086 167 15 : : PUNCT ejpam-3086 167 16 m m PROPN ejpam-3086 167 17 → → SYM ejpam-3086 167 18 m m PRON ejpam-3086 167 19 ´ ´ NOUN ejpam-3086 167 20 is be AUX ejpam-3086 167 21 a a DET ejpam-3086 167 22 harmonic harmonic ADJ ejpam-3086 167 23 map map NOUN ejpam-3086 167 24 . . PUNCT ejpam-3086 168 1 proof proof NOUN ejpam-3086 168 2 . . PUNCT ejpam-3086 169 1 let let VERB ejpam-3086 169 2 ∇ ∇ X ejpam-3086 169 3 be be AUX ejpam-3086 169 4 the the DET ejpam-3086 169 5 riemannian riemannian ADJ ejpam-3086 169 6 connection connection NOUN ejpam-3086 169 7 on on ADP ejpam-3086 169 8 m m PROPN ejpam-3086 169 9 . . PUNCT ejpam-3086 170 1 substituting substitute VERB ejpam-3086 170 2 y y PROPN ejpam-3086 170 3 by by ADP ejpam-3086 170 4 φx φx PROPN ejpam-3086 170 5 in in ADP ejpam-3086 170 6 ( ( PUNCT ejpam-3086 170 7 1 1 NUM ejpam-3086 170 8 ) ) PUNCT ejpam-3086 170 9 , , PUNCT ejpam-3086 170 10 we we PRON ejpam-3086 170 11 obtain obtain VERB ejpam-3086 170 12 : : PUNCT ejpam-3086 170 13 ( ( PUNCT ejpam-3086 170 14 ∇xφ)φx ∇xφ)φx X ejpam-3086 170 15 = = SYM ejpam-3086 170 16 ( ( PUNCT ejpam-3086 170 17 ∇φxφ)x ∇φxφ)x NOUN ejpam-3086 170 18 for for ADP ejpam-3086 170 19 any any DET ejpam-3086 170 20 x x SYM ejpam-3086 170 21 ∈ ∈ PROPN ejpam-3086 170 22 γ(d γ(d PROPN ejpam-3086 170 23 ) ) PUNCT ejpam-3086 170 24 in in ADP ejpam-3086 170 25 which which PRON ejpam-3086 170 26 d d NOUN ejpam-3086 170 27 = = PRON ejpam-3086 170 28 { { PUNCT ejpam-3086 170 29 x x PROPN ejpam-3086 170 30 ∈ ∈ PROPN ejpam-3086 170 31 tm tm NOUN ejpam-3086 170 32 ; ; PUNCT ejpam-3086 170 33 η(x η(x X ejpam-3086 170 34 ) ) PUNCT ejpam-3086 170 35 = = SYM ejpam-3086 170 36 0 0 NUM ejpam-3086 170 37 } } PUNCT ejpam-3086 170 38 , , PUNCT ejpam-3086 170 39 or or CCONJ ejpam-3086 170 40 equivalently equivalently ADV ejpam-3086 170 41 , , PUNCT ejpam-3086 170 42 ∇xx ∇xx PUNCT ejpam-3086 171 1 + + NOUN ejpam-3086 171 2 ∇φxφx ∇φxφx ADJ ejpam-3086 171 3 = = ADJ ejpam-3086 171 4 φ[φx φ[φx PROPN ejpam-3086 171 5 , , PUNCT ejpam-3086 171 6 x x NOUN ejpam-3086 171 7 ] ] PUNCT ejpam-3086 171 8 . . PUNCT ejpam-3086 172 1 let let VERB ejpam-3086 172 2 ∇f−1tḿ ∇f−1tḿ NOUN ejpam-3086 172 3 denotes denote VERB ejpam-3086 172 4 the the DET ejpam-3086 172 5 pull pull NOUN ejpam-3086 172 6 - - PUNCT ejpam-3086 172 7 back back NOUN ejpam-3086 172 8 of of ADP ejpam-3086 172 9 the the DET ejpam-3086 172 10 levi levi PROPN ejpam-3086 172 11 - - PUNCT ejpam-3086 172 12 civita civita PROPN ejpam-3086 172 13 connection connection NOUN ejpam-3086 172 14 ∇′ ∇′ NOUN ejpam-3086 172 15 on on ADP ejpam-3086 172 16 m´to m´to PROPN ejpam-3086 172 17 the the DET ejpam-3086 172 18 pullback pullback NOUN ejpam-3086 172 19 bundle bundle NOUN ejpam-3086 172 20 f−1tm´−→m f−1tm´−→m PROPN ejpam-3086 172 21 . . PUNCT ejpam-3086 173 1 since since SCONJ ejpam-3086 173 2 f f PROPN ejpam-3086 173 3 is be AUX ejpam-3086 173 4 ( ( PUNCT ejpam-3086 173 5 φ φ PROPN ejpam-3086 173 6 , , PUNCT ejpam-3086 173 7 φ́)-holomorphic φ́)-holomorphic ADJ ejpam-3086 173 8 , , PUNCT ejpam-3086 173 9 we we PRON ejpam-3086 173 10 also also ADV ejpam-3086 173 11 have have VERB ejpam-3086 173 12 on on ADP ejpam-3086 173 13 m m NOUN ejpam-3086 173 14 ´ ´ NOUN ejpam-3086 173 15 : : PUNCT ejpam-3086 174 1 ∇f ∇f PROPN ejpam-3086 174 2 −1tḿ −1tḿ PROPN ejpam-3086 174 3 x x SYM ejpam-3086 174 4 df(x df(x PRON ejpam-3086 174 5 ) ) PUNCT ejpam-3086 175 1 + + ADP ejpam-3086 175 2 ∇f ∇f PROPN ejpam-3086 175 3 −1tḿ −1tḿ PROPN ejpam-3086 175 4 φx φx ADJ ejpam-3086 175 5 df(φx df(φx NOUN ejpam-3086 175 6 ) ) PUNCT ejpam-3086 176 1 = = PUNCT ejpam-3086 177 1 φ́ φ́ PROPN ejpam-3086 178 1 [ [ X ejpam-3086 178 2 φ́ φ́ PROPN ejpam-3086 178 3 df(x df(x NOUN ejpam-3086 178 4 ) ) PUNCT ejpam-3086 178 5 , , PUNCT ejpam-3086 178 6 df(x df(x NOUN ejpam-3086 178 7 ) ) PUNCT ejpam-3086 178 8 ] ] PUNCT ejpam-3086 178 9 . . PUNCT ejpam-3086 179 1 references reference NOUN ejpam-3086 179 2 953 953 NUM ejpam-3086 179 3 if if SCONJ ejpam-3086 179 4 bf bf NOUN ejpam-3086 179 5 is be AUX ejpam-3086 179 6 the the DET ejpam-3086 179 7 second second ADJ ejpam-3086 179 8 fundamental fundamental ADJ ejpam-3086 179 9 form form NOUN ejpam-3086 179 10 of of ADP ejpam-3086 179 11 f f PROPN ejpam-3086 179 12 , , PUNCT ejpam-3086 179 13 that that PRON ejpam-3086 179 14 means mean VERB ejpam-3086 179 15 bf bf NOUN ejpam-3086 179 16 satisfies satisfie NOUN ejpam-3086 179 17 bf bf NOUN ejpam-3086 179 18 ( ( PUNCT ejpam-3086 179 19 x x X ejpam-3086 179 20 , , PUNCT ejpam-3086 179 21 y y PROPN ejpam-3086 179 22 ) ) PUNCT ejpam-3086 180 1 = = PUNCT ejpam-3086 180 2 ∇f ∇f PROPN ejpam-3086 180 3 −1tḿ −1tḿ NOUN ejpam-3086 180 4 y y NOUN ejpam-3086 180 5 df(x)− df(x)− PROPN ejpam-3086 180 6 df(∇xy df(∇xy PROPN ejpam-3086 180 7 ) ) PUNCT ejpam-3086 180 8 , , PUNCT ejpam-3086 180 9 it it PRON ejpam-3086 180 10 follows follow VERB ejpam-3086 180 11 that that SCONJ ejpam-3086 180 12 for for ADP ejpam-3086 180 13 any any DET ejpam-3086 180 14 x x SYM ejpam-3086 180 15 ∈ ∈ PROPN ejpam-3086 180 16 γ(d γ(d PROPN ejpam-3086 180 17 ) ) PUNCT ejpam-3086 180 18 , , PUNCT ejpam-3086 180 19 we we PRON ejpam-3086 180 20 have have VERB ejpam-3086 180 21 : : PUNCT ejpam-3086 180 22 bf bf NOUN ejpam-3086 180 23 ( ( PUNCT ejpam-3086 180 24 x x X ejpam-3086 180 25 , , PUNCT ejpam-3086 180 26 x x X ejpam-3086 180 27 ) ) PUNCT ejpam-3086 181 1 + + ADJ ejpam-3086 181 2 bf bf NOUN ejpam-3086 181 3 ( ( PUNCT ejpam-3086 181 4 φx φx PROPN ejpam-3086 181 5 , , PUNCT ejpam-3086 181 6 φx φx ADJ ejpam-3086 181 7 ) ) PUNCT ejpam-3086 181 8 = = SYM ejpam-3086 181 9 ∇f ∇f PROPN ejpam-3086 181 10 −1tḿ −1tḿ PROPN ejpam-3086 181 11 x x PUNCT ejpam-3086 181 12 df(x)− df(x)− PROPN ejpam-3086 181 13 df(∇xx df(∇xx PROPN ejpam-3086 181 14 ) ) PUNCT ejpam-3086 182 1 + + X ejpam-3086 182 2 ∇f ∇f PROPN ejpam-3086 182 3 −1tḿ −1tḿ X ejpam-3086 182 4 φx φx VERB ejpam-3086 182 5 df(φx)− df(φx)− PROPN ejpam-3086 182 6 df(∇φxφx df(∇φxφx PROPN ejpam-3086 182 7 ) ) PUNCT ejpam-3086 182 8 . . PUNCT ejpam-3086 183 1 = = PUNCT ejpam-3086 184 1 φ́ φ́ PROPN ejpam-3086 185 1 [ [ X ejpam-3086 185 2 φ́ φ́ PROPN ejpam-3086 185 3 df(x df(x NOUN ejpam-3086 185 4 ) ) PUNCT ejpam-3086 185 5 , , PUNCT ejpam-3086 185 6 df(x]− df(x]− PROPN ejpam-3086 185 7 dfφ[φx dfφ[φx PROPN ejpam-3086 185 8 , , PUNCT ejpam-3086 185 9 x x NOUN ejpam-3086 185 10 ] ] X ejpam-3086 185 11 = = SYM ejpam-3086 186 1 0 0 X ejpam-3086 186 2 . . PUNCT ejpam-3086 187 1 let let VERB ejpam-3086 187 2 ( ( PUNCT ejpam-3086 187 3 e1 e1 NOUN ejpam-3086 187 4 , , PUNCT ejpam-3086 187 5 ... ... PUNCT ejpam-3086 187 6 , , PUNCT ejpam-3086 187 7 en;φe1 en;φe1 VERB ejpam-3086 187 8 , , PUNCT ejpam-3086 187 9 ... ... PUNCT ejpam-3086 187 10 , , PUNCT ejpam-3086 187 11 φen φen PROPN ejpam-3086 187 12 , , PUNCT ejpam-3086 187 13 ξ ξ X ejpam-3086 187 14 ) ) PUNCT ejpam-3086 187 15 be be VERB ejpam-3086 187 16 a a DET ejpam-3086 187 17 local local ADJ ejpam-3086 187 18 orthonormal orthonormal ADJ ejpam-3086 187 19 φ φ NOUN ejpam-3086 187 20 - - NOUN ejpam-3086 187 21 basis basis NOUN ejpam-3086 187 22 where where SCONJ ejpam-3086 187 23 { { PUNCT ejpam-3086 187 24 ei ei NOUN ejpam-3086 187 25 , , PUNCT ejpam-3086 187 26 φei φei NOUN ejpam-3086 187 27 } } PUNCT ejpam-3086 187 28 ∈ ∈ PROPN ejpam-3086 187 29 γ(d γ(d PROPN ejpam-3086 187 30 ) ) PUNCT ejpam-3086 187 31 , , PUNCT ejpam-3086 187 32 then then ADV ejpam-3086 187 33 : : PUNCT ejpam-3086 187 34 τ(f τ(f PROPN ejpam-3086 187 35 ) ) PUNCT ejpam-3086 188 1 = = PRON ejpam-3086 188 2 σn σn X ejpam-3086 188 3 i=1bf i=1bf X ejpam-3086 188 4 ( ( PUNCT ejpam-3086 188 5 ei ei NOUN ejpam-3086 188 6 , , PUNCT ejpam-3086 188 7 ei ei NOUN ejpam-3086 188 8 ) ) PUNCT ejpam-3086 189 1 + + CCONJ ejpam-3086 189 2 σn σn PRON ejpam-3086 189 3 i=1bf i=1bf VERB ejpam-3086 189 4 ( ( PUNCT ejpam-3086 189 5 φei φei NOUN ejpam-3086 189 6 , , PUNCT ejpam-3086 189 7 φei φei NOUN ejpam-3086 189 8 ) ) PUNCT ejpam-3086 190 1 + + ADJ ejpam-3086 190 2 bf bf NOUN ejpam-3086 190 3 ( ( PUNCT ejpam-3086 190 4 ξ ξ PROPN ejpam-3086 190 5 , , PUNCT ejpam-3086 190 6 ξ ξ NOUN ejpam-3086 190 7 ) ) PUNCT ejpam-3086 190 8 = = SYM ejpam-3086 190 9 bf bf NOUN ejpam-3086 190 10 ( ( PUNCT ejpam-3086 190 11 ξ ξ PROPN ejpam-3086 190 12 , , PUNCT ejpam-3086 190 13 ξ ξ NOUN ejpam-3086 190 14 ) ) PUNCT ejpam-3086 190 15 . . PUNCT ejpam-3086 191 1 since since SCONJ ejpam-3086 191 2 dfoφ dfoφ NOUN ejpam-3086 191 3 = = NOUN ejpam-3086 191 4 ±φ́odf ±φ́odf NOUN ejpam-3086 191 5 , , PUNCT ejpam-3086 191 6 then then ADV ejpam-3086 191 7 φ́(df(ξ φ́(df(ξ NOUN ejpam-3086 191 8 ) ) PUNCT ejpam-3086 191 9 ) ) PUNCT ejpam-3086 191 10 = = SYM ejpam-3086 191 11 ±df(φξ ±df(φξ NOUN ejpam-3086 191 12 ) ) PUNCT ejpam-3086 191 13 = = SYM ejpam-3086 191 14 0 0 NUM ejpam-3086 191 15 , , PUNCT ejpam-3086 191 16 implies imply VERB ejpam-3086 191 17 that that SCONJ ejpam-3086 191 18 there there PRON ejpam-3086 191 19 exists exist VERB ejpam-3086 191 20 a a DET ejpam-3086 191 21 function function NOUN ejpam-3086 191 22 k k PROPN ejpam-3086 191 23 on on ADP ejpam-3086 191 24 m m PRON ejpam-3086 191 25 such such ADJ ejpam-3086 191 26 that that SCONJ ejpam-3086 191 27 dfx(ξx dfx(ξx NOUN ejpam-3086 191 28 ) ) PUNCT ejpam-3086 191 29 = = SYM ejpam-3086 191 30 k(x)ξ́f(x k(x)ξ́f(x PROPN ejpam-3086 191 31 ) ) PUNCT ejpam-3086 191 32 for for ADP ejpam-3086 191 33 any any DET ejpam-3086 191 34 x x SYM ejpam-3086 191 35 ∈m ∈m NOUN ejpam-3086 191 36 . . PUNCT ejpam-3086 192 1 on on ADP ejpam-3086 192 2 the the DET ejpam-3086 192 3 other other ADJ ejpam-3086 192 4 hand hand NOUN ejpam-3086 192 5 , , PUNCT ejpam-3086 192 6 by by ADP ejpam-3086 192 7 lemma lemma PROPN ejpam-3086 192 8 3.1(b 3.1(b NUM ejpam-3086 192 9 ) ) PUNCT ejpam-3086 192 10 , , PUNCT ejpam-3086 192 11 we we PRON ejpam-3086 192 12 have have VERB ejpam-3086 192 13 respectively respectively ADV ejpam-3086 192 14 on on ADP ejpam-3086 192 15 m m NOUN ejpam-3086 192 16 and and CCONJ ejpam-3086 192 17 m m PROPN ejpam-3086 192 18 , , PUNCT ejpam-3086 192 19 ́ ́ PROPN ejpam-3086 192 20 ∇ξξ ∇ξξ NOUN ejpam-3086 192 21 = = SYM ejpam-3086 192 22 0 0 NUM ejpam-3086 192 23 and and CCONJ ejpam-3086 192 24 ∇ξ́ξ́ ∇ξ́ξ́ PROPN ejpam-3086 192 25 = = SYM ejpam-3086 192 26 0 0 NUM ejpam-3086 192 27 , , PUNCT ejpam-3086 192 28 it it PRON ejpam-3086 192 29 follow follow VERB ejpam-3086 192 30 that that DET ejpam-3086 192 31 bf bf NOUN ejpam-3086 192 32 ( ( PUNCT ejpam-3086 192 33 ξ ξ PROPN ejpam-3086 192 34 , , PUNCT ejpam-3086 192 35 ξ ξ NOUN ejpam-3086 192 36 ) ) PUNCT ejpam-3086 192 37 = = SYM ejpam-3086 192 38 0 0 NUM ejpam-3086 192 39 and and CCONJ ejpam-3086 192 40 the the DET ejpam-3086 192 41 proof proof NOUN ejpam-3086 192 42 is be AUX ejpam-3086 192 43 complete complete ADJ ejpam-3086 192 44 . . PUNCT ejpam-3086 193 1 references reference NOUN ejpam-3086 193 2 [ [ X ejpam-3086 193 3 1 1 NUM ejpam-3086 193 4 ] ] PUNCT ejpam-3086 193 5 m. m. NOUN ejpam-3086 193 6 ahmad ahmad PROPN ejpam-3086 193 7 and and CCONJ ejpam-3086 193 8 m. m. NOUN ejpam-3086 193 9 danish danish ADJ ejpam-3086 193 10 siddiqui siddiqui PROPN ejpam-3086 193 11 , , PUNCT ejpam-3086 193 12 on on ADP ejpam-3086 193 13 a a DET ejpam-3086 193 14 nearly nearly ADV ejpam-3086 193 15 sasakian sasakian ADJ ejpam-3086 193 16 manifolds manifold NOUN ejpam-3086 193 17 with with ADP ejpam-3086 193 18 a a DET ejpam-3086 193 19 semisymmetric semisymmetric ADJ ejpam-3086 193 20 semi semi ADJ ejpam-3086 193 21 - - ADJ ejpam-3086 193 22 metric metric ADJ ejpam-3086 193 23 connection connection NOUN ejpam-3086 193 24 , , PUNCT ejpam-3086 193 25 int int NOUN ejpam-3086 193 26 . . PUNCT ejpam-3086 194 1 j. j. PROPN ejpam-3086 194 2 math math PROPN ejpam-3086 194 3 . . PUNCT ejpam-3086 195 1 analysis analysis NOUN ejpam-3086 195 2 . . PUNCT ejpam-3086 196 1 4(35)35 4(35)35 NOUN ejpam-3086 196 2 , , PUNCT ejpam-3086 196 3 1725 1725 NUM ejpam-3086 196 4 - - SYM ejpam-3086 196 5 1732 1732 NUM ejpam-3086 196 6 , , PUNCT ejpam-3086 196 7 2010 2010 NUM ejpam-3086 196 8 . . PUNCT ejpam-3086 197 1 [ [ X ejpam-3086 197 2 2 2 X ejpam-3086 197 3 ] ] PUNCT ejpam-3086 197 4 d. d. PROPN ejpam-3086 197 5 e. e. PROPN ejpam-3086 197 6 blair blair PROPN ejpam-3086 197 7 , , PUNCT ejpam-3086 197 8 contact contact NOUN ejpam-3086 197 9 manifolds manifold NOUN ejpam-3086 197 10 in in ADP ejpam-3086 197 11 riemannian riemannian ADJ ejpam-3086 197 12 geometry geometry NOUN ejpam-3086 197 13 . . PUNCT ejpam-3086 198 1 lecture lecture NOUN ejpam-3086 198 2 note note NOUN ejpam-3086 198 3 in in ADP ejpam-3086 198 4 math math NOUN ejpam-3086 198 5 , , PUNCT ejpam-3086 198 6 509 509 NUM ejpam-3086 198 7 , , PUNCT ejpam-3086 198 8 springer springer NOUN ejpam-3086 198 9 , , PUNCT ejpam-3086 198 10 1976 1976 NUM ejpam-3086 198 11 . . PUNCT ejpam-3086 199 1 [ [ X ejpam-3086 199 2 3 3 X ejpam-3086 199 3 ] ] X ejpam-3086 199 4 d. d. PROPN ejpam-3086 199 5 e. e. PROPN ejpam-3086 199 6 blair blair PROPN ejpam-3086 199 7 , , PUNCT ejpam-3086 199 8 riemannian riemannian ADJ ejpam-3086 199 9 geometry geometry NOUN ejpam-3086 199 10 of of ADP ejpam-3086 199 11 contact contact NOUN ejpam-3086 199 12 and and CCONJ ejpam-3086 199 13 symplectic symplectic ADJ ejpam-3086 199 14 manifolds manifold NOUN ejpam-3086 199 15 . . PUNCT ejpam-3086 199 16 progress progress NOUN ejpam-3086 199 17 in in ADP ejpam-3086 199 18 mathematics mathematic NOUN ejpam-3086 199 19 203 203 NUM ejpam-3086 199 20 , , PUNCT ejpam-3086 199 21 brikhauser brikhauser PROPN ejpam-3086 199 22 boston boston PROPN ejpam-3086 199 23 - - PUNCT ejpam-3086 199 24 basel basel PROPN ejpam-3086 199 25 - - PUNCT ejpam-3086 199 26 berlin berlin PROPN ejpam-3086 199 27 , , PUNCT ejpam-3086 199 28 2010 2010 NUM ejpam-3086 199 29 . . PUNCT ejpam-3086 200 1 [ [ X ejpam-3086 200 2 4 4 X ejpam-3086 200 3 ] ] X ejpam-3086 200 4 d. d. PROPN ejpam-3086 200 5 e. e. PROPN ejpam-3086 200 6 blair blair PROPN ejpam-3086 200 7 , , PUNCT ejpam-3086 200 8 d. d. PROPN ejpam-3086 200 9 k. k. PROPN ejpam-3086 200 10 showers showers PROPN ejpam-3086 200 11 and and CCONJ ejpam-3086 200 12 k. k. PROPN ejpam-3086 200 13 yano yano PROPN ejpam-3086 200 14 , , PUNCT ejpam-3086 200 15 nearly nearly ADV ejpam-3086 200 16 sasakian sasakian ADJ ejpam-3086 200 17 structures structure NOUN ejpam-3086 200 18 . . PUNCT ejpam-3086 201 1 kodai kodai PROPN ejpam-3086 201 2 math math PROPN ejpam-3086 201 3 . . PUNCT ejpam-3086 202 1 sem sem PROPN ejpam-3086 202 2 . . PUNCT ejpam-3086 202 3 rep rep PROPN ejpam-3086 202 4 . . PROPN ejpam-3086 202 5 27 27 NUM ejpam-3086 202 6 , , PUNCT ejpam-3086 202 7 175 175 NUM ejpam-3086 202 8 - - SYM ejpam-3086 202 9 180 180 NUM ejpam-3086 202 10 , , PUNCT ejpam-3086 202 11 1976 1976 NUM ejpam-3086 202 12 . . PUNCT ejpam-3086 203 1 [ [ X ejpam-3086 203 2 5 5 X ejpam-3086 203 3 ] ] PUNCT ejpam-3086 203 4 b. b. PROPN ejpam-3086 203 5 cappelletti cappelletti PROPN ejpam-3086 203 6 - - PUNCT ejpam-3086 203 7 montano montano PROPN ejpam-3086 203 8 and and CCONJ ejpam-3086 203 9 g. g. PROPN ejpam-3086 203 10 dileo dileo PROPN ejpam-3086 203 11 , , PUNCT ejpam-3086 203 12 nearly nearly ADV ejpam-3086 203 13 sasakian sasakian ADJ ejpam-3086 203 14 geometry geometry NOUN ejpam-3086 203 15 and and CCONJ ejpam-3086 203 16 su(2)structures su(2)structure NOUN ejpam-3086 203 17 . . PUNCT ejpam-3086 204 1 ann ann PROPN ejpam-3086 204 2 . . PROPN ejpam-3086 204 3 mat.pura mat.pura PROPN ejpam-3086 204 4 appl appl PROPN ejpam-3086 204 5 . . PUNCT ejpam-3086 205 1 ( ( PUNCT ejpam-3086 205 2 4 4 NUM ejpam-3086 205 3 ) ) PUNCT ejpam-3086 205 4 195 195 NUM ejpam-3086 205 5 , , PUNCT ejpam-3086 205 6 no no INTJ ejpam-3086 205 7 . . NOUN ejpam-3086 205 8 3 3 NUM ejpam-3086 205 9 , , PUNCT ejpam-3086 205 10 897922 897922 NUM ejpam-3086 205 11 , , PUNCT ejpam-3086 205 12 2016 2016 NUM ejpam-3086 205 13 . . PUNCT ejpam-3086 206 1 [ [ X ejpam-3086 206 2 6 6 NUM ejpam-3086 206 3 ] ] PUNCT ejpam-3086 206 4 s. s. PROPN ejpam-3086 206 5 tanno tanno PROPN ejpam-3086 206 6 , , PUNCT ejpam-3086 206 7 some some DET ejpam-3086 206 8 transformations transformation NOUN ejpam-3086 206 9 on on ADP ejpam-3086 206 10 manifolds manifold NOUN ejpam-3086 206 11 with with ADP ejpam-3086 206 12 almost almost ADV ejpam-3086 206 13 contact contact NOUN ejpam-3086 206 14 and and CCONJ ejpam-3086 206 15 contact contact VERB ejpam-3086 206 16 metric metric ADJ ejpam-3086 206 17 structures structure NOUN ejpam-3086 206 18 . . PUNCT ejpam-3086 207 1 tohoku tohoku PROPN ejpam-3086 207 2 . . PUNCT ejpam-3086 207 3 math math PROPN ejpam-3086 207 4 . . PUNCT ejpam-3086 208 1 j j PROPN ejpam-3086 208 2 , , PUNCT ejpam-3086 208 3 140 140 NUM ejpam-3086 208 4 - - SYM ejpam-3086 208 5 147 147 NUM ejpam-3086 208 6 , , PUNCT ejpam-3086 208 7 1963 1963 NUM ejpam-3086 208 8 . . PUNCT ejpam-3086 209 1 [ [ X ejpam-3086 209 2 7 7 X ejpam-3086 209 3 ] ] X ejpam-3086 209 4 l. l. PROPN ejpam-3086 209 5 s. s. PROPN ejpam-3086 209 6 das das PROPN ejpam-3086 209 7 , , PUNCT ejpam-3086 209 8 m. m. NOUN ejpam-3086 209 9 ahmad ahmad PROPN ejpam-3086 209 10 and and CCONJ ejpam-3086 209 11 a. a. NOUN ejpam-3086 209 12 haseeb haseeb PROPN ejpam-3086 209 13 , , PUNCT ejpam-3086 209 14 on on ADP ejpam-3086 209 15 semi semi ADJ ejpam-3086 209 16 - - ADJ ejpam-3086 209 17 invariant invariant ADJ ejpam-3086 209 18 submanifolds submanifold NOUN ejpam-3086 209 19 of of ADP ejpam-3086 209 20 a a DET ejpam-3086 209 21 nearly nearly ADV ejpam-3086 209 22 sasakian sasakian ADJ ejpam-3086 209 23 manifold manifold NOUN ejpam-3086 209 24 admitting admit VERB ejpam-3086 209 25 a a DET ejpam-3086 209 26 semi semi ADJ ejpam-3086 209 27 - - ADJ ejpam-3086 209 28 symmetric symmetric ADJ ejpam-3086 209 29 non non ADJ ejpam-3086 209 30 - - ADJ ejpam-3086 209 31 metric metric ADJ ejpam-3086 209 32 connection connection NOUN ejpam-3086 209 33 , , PUNCT ejpam-3086 209 34 journal journal NOUN ejpam-3086 209 35 of of ADP ejpam-3086 209 36 applied apply VERB ejpam-3086 209 37 analysis analysis NOUN ejpam-3086 209 38 17 17 NUM ejpam-3086 209 39 no no DET ejpam-3086 209 40 1 1 NUM ejpam-3086 209 41 , , PUNCT ejpam-3086 209 42 2011 2011 NUM ejpam-3086 209 43 . . PUNCT ejpam-3086 210 1 [ [ X ejpam-3086 210 2 8 8 X ejpam-3086 210 3 ] ] X ejpam-3086 210 4 j. j. PROPN ejpam-3086 210 5 eells eells PROPN ejpam-3086 210 6 and and CCONJ ejpam-3086 210 7 j. j. PROPN ejpam-3086 210 8 h. h. PROPN ejpam-3086 210 9 sampson sampson PROPN ejpam-3086 210 10 , , PUNCT ejpam-3086 210 11 harmonic harmonic ADJ ejpam-3086 210 12 mappings mapping NOUN ejpam-3086 210 13 of of ADP ejpam-3086 210 14 riemannian riemannian ADJ ejpam-3086 210 15 manifolds manifold NOUN ejpam-3086 210 16 . . PUNCT ejpam-3086 211 1 amer amer PROPN ejpam-3086 211 2 . . PUNCT ejpam-3086 212 1 j. j. PROPN ejpam-3086 212 2 math math PROPN ejpam-3086 212 3 . . PROPN ejpam-3086 213 1 86 86 NUM ejpam-3086 213 2 , , PUNCT ejpam-3086 213 3 109160 109160 NUM ejpam-3086 213 4 , , PUNCT ejpam-3086 213 5 1964 1964 NUM ejpam-3086 213 6 . . PUNCT ejpam-3086 214 1 [ [ X ejpam-3086 214 2 9 9 NUM ejpam-3086 214 3 ] ] PUNCT ejpam-3086 214 4 s. s. PROPN ejpam-3086 214 5 ianus ianus PROPN ejpam-3086 214 6 and and CCONJ ejpam-3086 214 7 a. a. NOUN ejpam-3086 214 8 m. m. PROPN ejpam-3086 214 9 pastore pastore PROPN ejpam-3086 214 10 , , PUNCT ejpam-3086 214 11 harmonic harmonic ADJ ejpam-3086 214 12 maps map NOUN ejpam-3086 214 13 on on ADP ejpam-3086 214 14 contact contact NOUN ejpam-3086 214 15 metric metric ADJ ejpam-3086 214 16 manifolds manifold NOUN ejpam-3086 214 17 . . PUNCT ejpam-3086 215 1 ann ann PROPN ejpam-3086 215 2 . . PUNCT ejpam-3086 216 1 math.blaise math.blaise PROPN ejpam-3086 216 2 pascal pascal PROPN ejpam-3086 216 3 , , PUNCT ejpam-3086 216 4 2 2 NUM ejpam-3086 216 5 , , PUNCT ejpam-3086 216 6 43 43 NUM ejpam-3086 216 7 - - SYM ejpam-3086 216 8 53 53 NUM ejpam-3086 216 9 , , PUNCT ejpam-3086 216 10 1995 1995 NUM ejpam-3086 216 11 . . PUNCT ejpam-3086 217 1 references reference NOUN ejpam-3086 217 2 954 954 NUM ejpam-3086 218 1 [ [ SYM ejpam-3086 218 2 10 10 NUM ejpam-3086 218 3 ] ] PUNCT ejpam-3086 218 4 j. j. PROPN ejpam-3086 218 5 h. h. PROPN ejpam-3086 218 6 kim kim PROPN ejpam-3086 218 7 , , PUNCT ejpam-3086 218 8 j.h j.h PROPN ejpam-3086 218 9 . . PROPN ejpam-3086 218 10 park park PROPN ejpam-3086 218 11 and and CCONJ ejpam-3086 218 12 k. k. PROPN ejpam-3086 218 13 sekigawa sekigawa PROPN ejpam-3086 218 14 , , PUNCT ejpam-3086 218 15 a a DET ejpam-3086 218 16 generalization generalization NOUN ejpam-3086 218 17 of of ADP ejpam-3086 218 18 contact contact NOUN ejpam-3086 218 19 metric metric ADJ ejpam-3086 218 20 manifolds manifold NOUN ejpam-3086 218 21 . . PUNCT ejpam-3086 219 1 balkan balkan PROPN ejpam-3086 219 2 j. j. PROPN ejpam-3086 219 3 geom geom PROPN ejpam-3086 219 4 . . PUNCT ejpam-3086 220 1 appl appl PROPN ejpam-3086 220 2 . . PROPN ejpam-3086 221 1 , , PUNCT ejpam-3086 221 2 v v NOUN ejpam-3086 221 3 19 19 NUM ejpam-3086 221 4 , , PUNCT ejpam-3086 221 5 no no DET ejpam-3086 221 6 2 2 NUM ejpam-3086 221 7 , , PUNCT ejpam-3086 221 8 2014 2014 NUM ejpam-3086 221 9 . . PUNCT ejpam-3086 222 1 [ [ X ejpam-3086 222 2 11 11 NUM ejpam-3086 222 3 ] ] PUNCT ejpam-3086 222 4 a. a. PROPN ejpam-3086 222 5 d. d. PROPN ejpam-3086 222 6 nicola nicola PROPN ejpam-3086 222 7 , , PUNCT ejpam-3086 222 8 g. g. PROPN ejpam-3086 222 9 dileo dileo PROPN ejpam-3086 222 10 and and CCONJ ejpam-3086 222 11 i. i. PROPN ejpam-3086 222 12 yudin yudin PROPN ejpam-3086 222 13 , , PUNCT ejpam-3086 222 14 nearly nearly ADV ejpam-3086 222 15 sasakian sasakian ADJ ejpam-3086 222 16 and and CCONJ ejpam-3086 222 17 nearly nearly ADV ejpam-3086 222 18 cosymplectic cosymplectic ADJ ejpam-3086 222 19 manifolds manifold NOUN ejpam-3086 222 20 . . PUNCT ejpam-3086 223 1 arxive arxive PROPN ejpam-3086 223 2 , , PUNCT ejpam-3086 223 3 2017 2017 NUM ejpam-3086 223 4 . . PUNCT ejpam-3086 224 1 [ [ X ejpam-3086 224 2 12 12 NUM ejpam-3086 224 3 ] ] PUNCT ejpam-3086 224 4 z. z. PROPN ejpam-3086 224 5 olszak olszak PROPN ejpam-3086 224 6 , , PUNCT ejpam-3086 224 7 nearly nearly ADV ejpam-3086 224 8 sasakian sasakian ADJ ejpam-3086 224 9 manifolds manifold NOUN ejpam-3086 224 10 , , PUNCT ejpam-3086 224 11 tensor(n.s tensor(n.s NOUN ejpam-3086 224 12 ) ) PUNCT ejpam-3086 224 13 . . PUNCT ejpam-3086 225 1 33 33 NUM ejpam-3086 225 2 no no NOUN ejpam-3086 225 3 . . NOUN ejpam-3086 226 1 3 3 NUM ejpam-3086 226 2 , , PUNCT ejpam-3086 226 3 277 277 NUM ejpam-3086 226 4 - - SYM ejpam-3086 226 5 286 286 NUM ejpam-3086 226 6 , , PUNCT ejpam-3086 226 7 1979 1979 NUM ejpam-3086 226 8 . . PUNCT ejpam-3086 227 1 [ [ X ejpam-3086 227 2 13 13 NUM ejpam-3086 227 3 ] ] PUNCT ejpam-3086 227 4 z. z. PROPN ejpam-3086 227 5 olszak olszak PROPN ejpam-3086 227 6 , , PUNCT ejpam-3086 227 7 five five NUM ejpam-3086 227 8 dimensional dimensional ADJ ejpam-3086 227 9 nearly nearly ADV ejpam-3086 227 10 sasakian sasakian ADJ ejpam-3086 227 11 manifols manifol NOUN ejpam-3086 227 12 , , PUNCT ejpam-3086 227 13 tensor(n.s tensor(n.s NOUN ejpam-3086 227 14 ) ) PUNCT ejpam-3086 227 15 . . PUNCT ejpam-3086 228 1 34 34 NUM ejpam-3086 228 2 no no NOUN ejpam-3086 228 3 . . NOUN ejpam-3086 229 1 3 3 NUM ejpam-3086 229 2 , , PUNCT ejpam-3086 229 3 273276 273276 NUM ejpam-3086 229 4 , , PUNCT ejpam-3086 229 5 1980 1980 NUM ejpam-3086 229 6 . . PUNCT ejpam-3086 230 1 [ [ X ejpam-3086 230 2 14 14 NUM ejpam-3086 230 3 ] ] X ejpam-3086 230 4 s. s. PROPN ejpam-3086 230 5 sasaki sasaki PROPN ejpam-3086 230 6 , , PUNCT ejpam-3086 230 7 on on ADP ejpam-3086 230 8 differentiable differentiable ADJ ejpam-3086 230 9 manifolds manifold NOUN ejpam-3086 230 10 with with ADP ejpam-3086 230 11 certain certain ADJ ejpam-3086 230 12 structures structure NOUN ejpam-3086 230 13 which which PRON ejpam-3086 230 14 are be AUX ejpam-3086 230 15 closely closely ADV ejpam-3086 230 16 related relate VERB ejpam-3086 230 17 to to ADP ejpam-3086 230 18 almost almost ADV ejpam-3086 230 19 contact contact VERB ejpam-3086 230 20 structures structure NOUN ejpam-3086 230 21 , , PUNCT ejpam-3086 230 22 tohoku tohoku PROPN ejpam-3086 230 23 math math PROPN ejpam-3086 230 24 . . PUNCT ejpam-3086 231 1 j. j. PROPN ejpam-3086 231 2 , , PUNCT ejpam-3086 231 3 12 12 NUM ejpam-3086 231 4 , , PUNCT ejpam-3086 231 5 459 459 NUM ejpam-3086 231 6 - - SYM ejpam-3086 231 7 476 476 NUM ejpam-3086 231 8 , , PUNCT ejpam-3086 231 9 1960 1960 NUM ejpam-3086 231 10 . . PUNCT ejpam-3086 232 1 [ [ X ejpam-3086 232 2 15 15 NUM ejpam-3086 232 3 ] ] X ejpam-3086 232 4 m. m. NOUN ejpam-3086 232 5 h. h. PROPN ejpam-3086 232 6 shahid shahid PROPN ejpam-3086 232 7 , , PUNCT ejpam-3086 232 8 on on ADP ejpam-3086 232 9 semiinvariant semiinvariant ADJ ejpam-3086 232 10 submanifolds submanifold NOUN ejpam-3086 232 11 of of ADP ejpam-3086 232 12 a a DET ejpam-3086 232 13 nearly nearly ADV ejpam-3086 232 14 sasakian sasakian ADJ ejpam-3086 232 15 manifold manifold ADJ ejpam-3086 232 16 , , PUNCT ejpam-3086 232 17 indian indian PROPN ejpam-3086 232 18 . . PUNCT ejpam-3086 233 1 j. j. PROPN ejpam-3086 233 2 pure pure PROPN ejpam-3086 233 3 . . PUNCT ejpam-3086 234 1 apple apple PROPN ejpam-3086 234 2 . . PUNCT ejpam-3086 235 1 math math NOUN ejpam-3086 235 2 . . PUNCT ejpam-3086 236 1 vol vol NOUN ejpam-3086 236 2 24 24 NUM ejpam-3086 236 3 , , PUNCT ejpam-3086 236 4 f.2 f.2 PROPN ejpam-3086 236 5 , , PUNCT ejpam-3086 236 6 1999 1999 NUM ejpam-3086 236 7 . . PUNCT ejpam-3086 237 1 [ [ X ejpam-3086 237 2 16 16 X ejpam-3086 237 3 ] ] X ejpam-3086 237 4 y. y. PROPN ejpam-3086 237 5 tashiro tashiro PROPN ejpam-3086 237 6 , , PUNCT ejpam-3086 237 7 on on ADP ejpam-3086 237 8 contact contact NOUN ejpam-3086 237 9 structure structure NOUN ejpam-3086 237 10 of of ADP ejpam-3086 237 11 hypersurfaces hypersurface NOUN ejpam-3086 237 12 in in ADP ejpam-3086 237 13 complex complex ADJ ejpam-3086 237 14 manifold manifold PROPN ejpam-3086 237 15 ii ii PROPN ejpam-3086 237 16 . . PUNCT ejpam-3086 238 1 tohoku tohoku PROPN ejpam-3086 238 2 math math PROPN ejpam-3086 238 3 j. j. PROPN ejpam-3086 238 4 1963 1963 NUM ejpam-3086 238 5 . . PUNCT