id sid tid token lemma pos ejpam-587 1 1 12_587_abood.dvi 12_587_abood.dvi NUM ejpam-587 1 2 european european PROPN ejpam-587 1 3 journal journal PROPN ejpam-587 1 4 of of ADP ejpam-587 1 5 pure pure ADJ ejpam-587 1 6 and and CCONJ ejpam-587 1 7 applied apply VERB ejpam-587 1 8 mathematics mathematic NOUN ejpam-587 1 9 vol vol NOUN ejpam-587 1 10 . . PUNCT ejpam-587 2 1 3 3 NUM ejpam-587 2 2 , , PUNCT ejpam-587 2 3 no no INTJ ejpam-587 2 4 . . NOUN ejpam-587 2 5 4 4 NUM ejpam-587 2 6 , , PUNCT ejpam-587 2 7 2010 2010 NUM ejpam-587 2 8 , , PUNCT ejpam-587 2 9 730 730 NUM ejpam-587 2 10 - - SYM ejpam-587 2 11 736 736 NUM ejpam-587 2 12 issn issn PROPN ejpam-587 2 13 1307 1307 NUM ejpam-587 2 14 - - SYM ejpam-587 2 15 5543 5543 NUM ejpam-587 2 16 – – PUNCT ejpam-587 2 17 www.ejpam.com www.ejpam.com X ejpam-587 2 18 almost almost ADV ejpam-587 2 19 hermitian hermitian PROPN ejpam-587 2 20 manifold manifold ADJ ejpam-587 2 21 with with ADP ejpam-587 2 22 flat flat ADJ ejpam-587 2 23 bochner bochner NOUN ejpam-587 2 24 tensor tensor NOUN ejpam-587 2 25 habeeb habeeb PROPN ejpam-587 2 26 m. m. PROPN ejpam-587 2 27 abood abood PROPN ejpam-587 2 28 department department PROPN ejpam-587 2 29 of of ADP ejpam-587 2 30 mathematics mathematics PROPN ejpam-587 2 31 , , PUNCT ejpam-587 2 32 university university PROPN ejpam-587 2 33 of of ADP ejpam-587 2 34 basrah basrah PROPN ejpam-587 2 35 , , PUNCT ejpam-587 2 36 basrah basrah PROPN ejpam-587 2 37 - - PUNCT ejpam-587 2 38 iraq iraq PROPN ejpam-587 2 39 abstract abstract NOUN ejpam-587 2 40 . . PUNCT ejpam-587 3 1 many many ADJ ejpam-587 3 2 researchers researcher NOUN ejpam-587 3 3 investigated investigate VERB ejpam-587 3 4 the the DET ejpam-587 3 5 flat flat ADJ ejpam-587 3 6 bochner bochner NOUN ejpam-587 3 7 tensor tensor NOUN ejpam-587 3 8 on on ADP ejpam-587 3 9 some some DET ejpam-587 3 10 kinds kind NOUN ejpam-587 3 11 of of ADP ejpam-587 3 12 almost almost ADV ejpam-587 3 13 hermitian hermitian ADJ ejpam-587 3 14 manifold manifold NOUN ejpam-587 3 15 . . PUNCT ejpam-587 4 1 in in ADP ejpam-587 4 2 the the DET ejpam-587 4 3 present present ADJ ejpam-587 4 4 paper paper NOUN ejpam-587 4 5 the the DET ejpam-587 4 6 author author NOUN ejpam-587 4 7 studies study VERB ejpam-587 4 8 this this DET ejpam-587 4 9 tensor tensor NOUN ejpam-587 4 10 on on ADP ejpam-587 4 11 general general ADJ ejpam-587 4 12 class class NOUN ejpam-587 4 13 almost almost ADV ejpam-587 4 14 hermitian hermitian ADJ ejpam-587 4 15 manifold manifold ADJ ejpam-587 4 16 by by ADP ejpam-587 4 17 using use VERB ejpam-587 4 18 a a DET ejpam-587 4 19 new new ADJ ejpam-587 4 20 methodology methodology NOUN ejpam-587 4 21 which which PRON ejpam-587 4 22 is be AUX ejpam-587 4 23 called call VERB ejpam-587 4 24 an an DET ejpam-587 4 25 adjoint adjoint NOUN ejpam-587 4 26 g g NOUN ejpam-587 4 27 - - PUNCT ejpam-587 4 28 structure structure NOUN ejpam-587 4 29 space space NOUN ejpam-587 4 30 . . PUNCT ejpam-587 5 1 thus thus ADV ejpam-587 5 2 this this DET ejpam-587 5 3 study study NOUN ejpam-587 5 4 generalize generalize VERB ejpam-587 5 5 the the DET ejpam-587 5 6 results result NOUN ejpam-587 5 7 which which PRON ejpam-587 5 8 are be AUX ejpam-587 5 9 found find VERB ejpam-587 5 10 out out ADP ejpam-587 5 11 by by ADP ejpam-587 5 12 those those DET ejpam-587 5 13 researchers researcher NOUN ejpam-587 5 14 . . PUNCT ejpam-587 6 1 it it PRON ejpam-587 6 2 is be AUX ejpam-587 6 3 proved prove VERB ejpam-587 6 4 that that SCONJ ejpam-587 6 5 if if SCONJ ejpam-587 6 6 m m NOUN ejpam-587 6 7 is be AUX ejpam-587 6 8 an an DET ejpam-587 6 9 almost almost ADV ejpam-587 6 10 hermitian hermitian ADJ ejpam-587 6 11 manifold manifold NOUN ejpam-587 6 12 of of ADP ejpam-587 6 13 class class NOUN ejpam-587 6 14 r1 r1 NOUN ejpam-587 6 15 with with ADP ejpam-587 6 16 flat flat ADJ ejpam-587 6 17 bochner bochner NOUN ejpam-587 6 18 tensor tensor NOUN ejpam-587 6 19 , , PUNCT ejpam-587 6 20 then then ADV ejpam-587 6 21 either either CCONJ ejpam-587 6 22 m m NOUN ejpam-587 6 23 is be AUX ejpam-587 6 24 2 2 NUM ejpam-587 6 25 - - PUNCT ejpam-587 6 26 dimensional dimensional ADJ ejpam-587 6 27 flat flat ADJ ejpam-587 6 28 ricci ricci NOUN ejpam-587 6 29 manifold manifold NOUN ejpam-587 6 30 or or CCONJ ejpam-587 6 31 n n CCONJ ejpam-587 6 32 - - PUNCT ejpam-587 6 33 dimensional dimensional ADJ ejpam-587 6 34 ( ( PUNCT ejpam-587 6 35 n n CCONJ ejpam-587 6 36 > > X ejpam-587 6 37 2 2 NUM ejpam-587 6 38 ) ) PUNCT ejpam-587 6 39 flat flat ADJ ejpam-587 6 40 scalar scalar ADJ ejpam-587 6 41 curvature curvature NOUN ejpam-587 6 42 tensor tensor NOUN ejpam-587 6 43 manifold manifold NOUN ejpam-587 6 44 . . PUNCT ejpam-587 7 1 as as ADV ejpam-587 7 2 well well ADV ejpam-587 7 3 , , PUNCT ejpam-587 7 4 it it PRON ejpam-587 7 5 is be AUX ejpam-587 7 6 proved prove VERB ejpam-587 7 7 that that SCONJ ejpam-587 7 8 if if SCONJ ejpam-587 7 9 m m NOUN ejpam-587 7 10 is be AUX ejpam-587 7 11 an an DET ejpam-587 7 12 almost almost ADV ejpam-587 7 13 hermitian hermitian ADJ ejpam-587 7 14 manifold manifold ADJ ejpam-587 7 15 with with ADP ejpam-587 7 16 flat flat ADJ ejpam-587 7 17 bochner bochner NOUN ejpam-587 7 18 tensor tensor NOUN ejpam-587 7 19 , , PUNCT ejpam-587 7 20 then then ADV ejpam-587 7 21 m m VERB ejpam-587 7 22 is be AUX ejpam-587 7 23 a a DET ejpam-587 7 24 manifold manifold NOUN ejpam-587 7 25 of of ADP ejpam-587 7 26 class class NOUN ejpam-587 7 27 r3 r3 PROPN ejpam-587 7 28 if if SCONJ ejpam-587 8 1 and and CCONJ ejpam-587 8 2 only only ADV ejpam-587 8 3 if if SCONJ ejpam-587 8 4 m m NOUN ejpam-587 8 5 is be AUX ejpam-587 8 6 a a DET ejpam-587 8 7 linear linear ADJ ejpam-587 8 8 complex complex ADJ ejpam-587 8 9 manifold manifold NOUN ejpam-587 8 10 . . PUNCT ejpam-587 9 1 later later ADV ejpam-587 9 2 on on ADV ejpam-587 9 3 , , PUNCT ejpam-587 9 4 equivalently equivalently ADV ejpam-587 9 5 of of ADP ejpam-587 9 6 classes class NOUN ejpam-587 9 7 r2 r2 PROPN ejpam-587 9 8 and and CCONJ ejpam-587 9 9 r3 r3 PROPN ejpam-587 9 10 is be AUX ejpam-587 9 11 investigated investigate VERB ejpam-587 9 12 . . PUNCT ejpam-587 10 1 finally finally ADV ejpam-587 10 2 we we PRON ejpam-587 10 3 prove prove VERB ejpam-587 10 4 that that SCONJ ejpam-587 10 5 if if SCONJ ejpam-587 10 6 m m NOUN ejpam-587 10 7 is be AUX ejpam-587 10 8 flat flat ADJ ejpam-587 10 9 manifold manifold ADJ ejpam-587 10 10 with with ADP ejpam-587 10 11 flat flat ADJ ejpam-587 10 12 bochner bochner NOUN ejpam-587 10 13 tensor tensor NOUN ejpam-587 10 14 , , PUNCT ejpam-587 10 15 then then ADV ejpam-587 10 16 m m NOUN ejpam-587 10 17 is be AUX ejpam-587 10 18 an an DET ejpam-587 10 19 einstein einstein NOUN ejpam-587 10 20 manifold manifold NOUN ejpam-587 10 21 with with ADP ejpam-587 10 22 a a DET ejpam-587 10 23 cosmological cosmological ADJ ejpam-587 10 24 constant constant ADJ ejpam-587 10 25 . . PUNCT ejpam-587 11 1 2000 2000 NUM ejpam-587 11 2 mathematics mathematic NOUN ejpam-587 11 3 subject subject NOUN ejpam-587 11 4 classifications classification NOUN ejpam-587 11 5 : : PUNCT ejpam-587 11 6 53c55 53c55 NUM ejpam-587 11 7 , , PUNCT ejpam-587 11 8 53b35 53b35 NUM ejpam-587 11 9 key key ADJ ejpam-587 11 10 words word NOUN ejpam-587 11 11 and and CCONJ ejpam-587 11 12 phrases phrase NOUN ejpam-587 11 13 : : PUNCT ejpam-587 11 14 almost almost ADV ejpam-587 11 15 hermitian hermitian ADJ ejpam-587 11 16 manifold manifold ADJ ejpam-587 11 17 , , PUNCT ejpam-587 11 18 flat flat ADJ ejpam-587 11 19 bochner bochner NOUN ejpam-587 11 20 tensor tensor NOUN ejpam-587 11 21 , , PUNCT ejpam-587 11 22 adjoint adjoint VERB ejpam-587 11 23 g g NOUN ejpam-587 11 24 - - PUNCT ejpam-587 11 25 structure structure NOUN ejpam-587 11 26 space space NOUN ejpam-587 11 27 . . PUNCT ejpam-587 12 1 1 1 X ejpam-587 12 2 . . X ejpam-587 12 3 introduction introduction NOUN ejpam-587 12 4 the the DET ejpam-587 12 5 bochner bochner NOUN ejpam-587 12 6 tensor tensor NOUN ejpam-587 12 7 was be AUX ejpam-587 12 8 introduced introduce VERB ejpam-587 12 9 by by ADP ejpam-587 12 10 s. s. PROPN ejpam-587 12 11 bochner bochner PROPN ejpam-587 13 1 [ [ X ejpam-587 13 2 3 3 NUM ejpam-587 13 3 ] ] PUNCT ejpam-587 13 4 . . PUNCT ejpam-587 14 1 he he PRON ejpam-587 14 2 defined define VERB ejpam-587 14 3 this this DET ejpam-587 14 4 tensor tensor NOUN ejpam-587 14 5 on on ADP ejpam-587 14 6 a a DET ejpam-587 14 7 kahler kahler NOUN ejpam-587 14 8 manifold manifold ADJ ejpam-587 14 9 as as ADP ejpam-587 14 10 a a DET ejpam-587 14 11 formal formal ADJ ejpam-587 14 12 analogy analogy NOUN ejpam-587 14 13 of of ADP ejpam-587 14 14 the the DET ejpam-587 14 15 weyle weyle PROPN ejpam-587 14 16 conformal conformal PROPN ejpam-587 14 17 curvature curvature PROPN ejpam-587 14 18 tensor tensor NOUN ejpam-587 14 19 . . PUNCT ejpam-587 15 1 s. s. PROPN ejpam-587 15 2 tachibana tachibana PROPN ejpam-587 16 1 [ [ X ejpam-587 16 2 14 14 NUM ejpam-587 16 3 ] ] PUNCT ejpam-587 16 4 gave give VERB ejpam-587 16 5 it it PRON ejpam-587 16 6 the the DET ejpam-587 16 7 real real ADJ ejpam-587 16 8 form form NOUN ejpam-587 16 9 and and CCONJ ejpam-587 16 10 he he PRON ejpam-587 16 11 proved prove VERB ejpam-587 16 12 that that SCONJ ejpam-587 16 13 the the DET ejpam-587 16 14 bochner bochner NOUN ejpam-587 16 15 tensor tensor NOUN ejpam-587 16 16 had have VERB ejpam-587 16 17 a a DET ejpam-587 16 18 meaning meaning NOUN ejpam-587 16 19 on on ADP ejpam-587 16 20 any any DET ejpam-587 16 21 almost almost ADV ejpam-587 16 22 hermitian hermitian ADJ ejpam-587 16 23 manifold manifold NOUN ejpam-587 16 24 . . PUNCT ejpam-587 17 1 the the DET ejpam-587 17 2 kahler kahler NOUN ejpam-587 17 3 manifold manifold VERB ejpam-587 17 4 with with ADP ejpam-587 17 5 flat flat ADJ ejpam-587 17 6 bochner bochner NOUN ejpam-587 17 7 curvature curvature NOUN ejpam-587 17 8 tensor tensor NOUN ejpam-587 17 9 has have AUX ejpam-587 17 10 been be AUX ejpam-587 17 11 studied study VERB ejpam-587 17 12 by by ADP ejpam-587 17 13 many many ADJ ejpam-587 17 14 researchers researcher NOUN ejpam-587 17 15 . . PUNCT ejpam-587 18 1 m. m. NOUN ejpam-587 18 2 mastumoto mastumoto PROPN ejpam-587 19 1 [ [ X ejpam-587 19 2 8 8 NUM ejpam-587 19 3 ] ] PUNCT ejpam-587 19 4 proved prove VERB ejpam-587 19 5 that that SCONJ ejpam-587 19 6 a a DET ejpam-587 19 7 kahler kahler NOUN ejpam-587 19 8 manifold manifold NOUN ejpam-587 19 9 of of ADP ejpam-587 19 10 constant constant ADJ ejpam-587 19 11 scalar scalar ADJ ejpam-587 19 12 curvature curvature NOUN ejpam-587 19 13 tensor tensor NOUN ejpam-587 19 14 with with ADP ejpam-587 19 15 flat flat ADJ ejpam-587 19 16 bochner bochner NOUN ejpam-587 19 17 tensor tensor NOUN ejpam-587 19 18 is be AUX ejpam-587 19 19 local local ADJ ejpam-587 19 20 symmetric symmetric NOUN ejpam-587 19 21 . . PUNCT ejpam-587 20 1 s. s. PROPN ejpam-587 20 2 tachibana tachibana PROPN ejpam-587 21 1 [ [ X ejpam-587 21 2 15 15 NUM ejpam-587 21 3 ] ] PUNCT ejpam-587 21 4 proved prove VERB ejpam-587 21 5 that that SCONJ ejpam-587 21 6 kahler kahler NOUN ejpam-587 21 7 manifold manifold ADJ ejpam-587 21 8 of of ADP ejpam-587 21 9 a a DET ejpam-587 21 10 constant constant ADJ ejpam-587 21 11 scalar scalar ADJ ejpam-587 21 12 curvature curvature NOUN ejpam-587 21 13 tensor tensor NOUN ejpam-587 21 14 with with ADP ejpam-587 21 15 flat flat ADJ ejpam-587 21 16 bochner bochner NOUN ejpam-587 21 17 tensor tensor NOUN ejpam-587 21 18 is be AUX ejpam-587 21 19 local local ADJ ejpam-587 21 20 - - PUNCT ejpam-587 21 21 isometric isometric ADJ ejpam-587 21 22 to to ADP ejpam-587 21 23 the the DET ejpam-587 21 24 product product NOUN ejpam-587 21 25 of of ADP ejpam-587 21 26 complex complex ADJ ejpam-587 21 27 spaces space NOUN ejpam-587 21 28 . . PUNCT ejpam-587 22 1 l. l. PROPN ejpam-587 22 2 vanhecke vanhecke PROPN ejpam-587 23 1 [ [ X ejpam-587 23 2 18 18 NUM ejpam-587 23 3 ] ] PUNCT ejpam-587 23 4 studied study VERB ejpam-587 23 5 the the DET ejpam-587 23 6 bochner bochner NOUN ejpam-587 23 7 curvature curvature NOUN ejpam-587 23 8 tensor tensor NOUN ejpam-587 23 9 on on ADP ejpam-587 23 10 almost almost ADV ejpam-587 23 11 hermitian hermitian ADJ ejpam-587 23 12 manifold manifold NOUN ejpam-587 23 13 and and CCONJ ejpam-587 23 14 he he PRON ejpam-587 23 15 obtained obtain VERB ejpam-587 23 16 some some DET ejpam-587 23 17 properties property NOUN ejpam-587 23 18 which which PRON ejpam-587 23 19 are be AUX ejpam-587 23 20 proved prove VERB ejpam-587 23 21 for for ADP ejpam-587 23 22 kahler kahler NOUN ejpam-587 23 23 manifold manifold NOUN ejpam-587 23 24 . . PUNCT ejpam-587 24 1 z. z. PROPN ejpam-587 24 2 olsgak olsgak PROPN ejpam-587 25 1 [ [ X ejpam-587 25 2 10 10 NUM ejpam-587 25 3 ] ] PUNCT ejpam-587 25 4 gave give VERB ejpam-587 25 5 the the DET ejpam-587 25 6 classification classification NOUN ejpam-587 25 7 of of ADP ejpam-587 25 8 4 4 NUM ejpam-587 25 9 - - PUNCT ejpam-587 25 10 dimensional dimensional ADJ ejpam-587 25 11 compact compact ADJ ejpam-587 25 12 flat flat ADJ ejpam-587 25 13 bochner bochner NOUN ejpam-587 25 14 of of ADP ejpam-587 25 15 kahler kahler NOUN ejpam-587 25 16 manifold manifold ADJ ejpam-587 25 17 with with ADP ejpam-587 25 18 non non X ejpam-587 25 19 positive positive ADJ ejpam-587 25 20 scalar scalar ADJ ejpam-587 25 21 curvature curvature NOUN ejpam-587 25 22 tensor tensor NOUN ejpam-587 25 23 . . PUNCT ejpam-587 26 1 m. m. PROPN ejpam-587 26 2 petrovic petrovic PROPN ejpam-587 26 3 and and CCONJ ejpam-587 26 4 l. l. PROPN ejpam-587 26 5 vestraclen vestraclen PROPN ejpam-587 27 1 [ [ X ejpam-587 27 2 11 11 NUM ejpam-587 27 3 ] ] PUNCT ejpam-587 27 4 studied study VERB ejpam-587 27 5 the the DET ejpam-587 27 6 flat flat ADJ ejpam-587 27 7 bochner bochner NOUN ejpam-587 27 8 of of ADP ejpam-587 27 9 kahler kahler NOUN ejpam-587 27 10 manifold manifold ADJ ejpam-587 27 11 where where SCONJ ejpam-587 27 12 the the DET ejpam-587 27 13 weyles weyle NOUN ejpam-587 27 14 tensor tensor NOUN ejpam-587 27 15 satisfies satisfy VERB ejpam-587 27 16 some some DET ejpam-587 27 17 conditions condition NOUN ejpam-587 27 18 . . PUNCT ejpam-587 28 1 k. k. PROPN ejpam-587 28 2 nam nam PROPN ejpam-587 29 1 [ [ X ejpam-587 29 2 9 9 NUM ejpam-587 29 3 ] ] PUNCT ejpam-587 29 4 proved prove VERB ejpam-587 29 5 that that SCONJ ejpam-587 29 6 if if SCONJ ejpam-587 29 7 m m NOUN ejpam-587 29 8 is be AUX ejpam-587 29 9 a a DET ejpam-587 29 10 kahler kahler NOUN ejpam-587 29 11 manifold manifold ADJ ejpam-587 29 12 with with ADP ejpam-587 29 13 flat flat ADJ ejpam-587 29 14 bochner bochner NOUN ejpam-587 29 15 curvature curvature NOUN ejpam-587 29 16 tensor tensor NOUN ejpam-587 29 17 whose whose DET ejpam-587 29 18 length length NOUN ejpam-587 29 19 of of ADP ejpam-587 29 20 the the DET ejpam-587 29 21 ricci ricci PROPN ejpam-587 29 22 tensor tensor NOUN ejpam-587 29 23 is be AUX ejpam-587 29 24 constant constant ADJ ejpam-587 29 25 , , PUNCT ejpam-587 29 26 then then ADV ejpam-587 29 27 m m VERB ejpam-587 29 28 is be AUX ejpam-587 29 29 a a DET ejpam-587 29 30 space space NOUN ejpam-587 29 31 of of ADP ejpam-587 29 32 constant constant ADJ ejpam-587 29 33 holomorphic holomorphic ADJ ejpam-587 29 34 sectional sectional ADJ ejpam-587 29 35 curvature curvature NOUN ejpam-587 29 36 email email NOUN ejpam-587 29 37 address address NOUN ejpam-587 29 38 : : PUNCT ejpam-587 29 39 iraqsafwan iraqsafwan PROPN ejpam-587 29 40 � � PROPN ejpam-587 29 41 yahoo yahoo PROPN ejpam-587 29 42 . . PUNCT ejpam-587 30 1 om om PROPN ejpam-587 30 2 ( ( PUNCT ejpam-587 30 3 h. h. PROPN ejpam-587 30 4 abood abood PROPN ejpam-587 30 5 ) ) PUNCT ejpam-587 30 6 http://www.ejpam.com http://www.ejpam.com X ejpam-587 31 1 730 730 NUM ejpam-587 31 2 c c X ejpam-587 31 3 © © PROPN ejpam-587 31 4 2010 2010 NUM ejpam-587 31 5 ejpam ejpam NOUN ejpam-587 31 6 all all DET ejpam-587 31 7 rights right NOUN ejpam-587 31 8 reserved reserve VERB ejpam-587 31 9 . . PUNCT ejpam-587 32 1 h. h. PROPN ejpam-587 32 2 abood abood PROPN ejpam-587 32 3 / / SYM ejpam-587 32 4 eur eur PROPN ejpam-587 32 5 . . PUNCT ejpam-587 33 1 j. j. PROPN ejpam-587 33 2 pure pure PROPN ejpam-587 33 3 appl appl PROPN ejpam-587 33 4 . . PROPN ejpam-587 33 5 math math PROPN ejpam-587 33 6 , , PUNCT ejpam-587 33 7 3 3 NUM ejpam-587 33 8 ( ( PUNCT ejpam-587 33 9 2010 2010 NUM ejpam-587 33 10 ) ) PUNCT ejpam-587 33 11 , , PUNCT ejpam-587 33 12 730 730 NUM ejpam-587 33 13 - - SYM ejpam-587 33 14 736 736 NUM ejpam-587 33 15 731 731 NUM ejpam-587 33 16 or or CCONJ ejpam-587 33 17 a a DET ejpam-587 33 18 locally locally ADV ejpam-587 33 19 product product NOUN ejpam-587 33 20 space space NOUN ejpam-587 33 21 of of ADP ejpam-587 33 22 two two NUM ejpam-587 33 23 spaces space NOUN ejpam-587 33 24 of of ADP ejpam-587 33 25 constant constant ADJ ejpam-587 33 26 holomorphic holomorphic ADJ ejpam-587 33 27 sectional sectional ADJ ejpam-587 33 28 curvatures curvature NOUN ejpam-587 33 29 . . PUNCT ejpam-587 34 1 a. a. PROPN ejpam-587 34 2 al al PROPN ejpam-587 34 3 - - PUNCT ejpam-587 34 4 otman otman NOUN ejpam-587 34 5 [ [ X ejpam-587 34 6 1 1 X ejpam-587 34 7 ] ] PUNCT ejpam-587 34 8 studied study VERB ejpam-587 34 9 the the DET ejpam-587 34 10 bochner bochner NOUN ejpam-587 34 11 tensor tensor NOUN ejpam-587 34 12 of of ADP ejpam-587 34 13 the the DET ejpam-587 34 14 class class NOUN ejpam-587 34 15 nearly nearly ADV ejpam-587 34 16 kahler kahler NOUN ejpam-587 34 17 manifold manifold NOUN ejpam-587 34 18 . . PUNCT ejpam-587 35 1 he he PRON ejpam-587 35 2 found find VERB ejpam-587 35 3 the the DET ejpam-587 35 4 classification classification NOUN ejpam-587 35 5 of of ADP ejpam-587 35 6 the the DET ejpam-587 35 7 flat flat ADJ ejpam-587 35 8 bochner bochner NOUN ejpam-587 35 9 tensor tensor NOUN ejpam-587 35 10 of of ADP ejpam-587 35 11 this this DET ejpam-587 35 12 class class NOUN ejpam-587 35 13 . . PUNCT ejpam-587 36 1 in in ADP ejpam-587 36 2 fact fact NOUN ejpam-587 36 3 you you PRON ejpam-587 36 4 may may AUX ejpam-587 36 5 notice notice VERB ejpam-587 36 6 that that SCONJ ejpam-587 36 7 the the DET ejpam-587 36 8 most most ADJ ejpam-587 36 9 of of ADP ejpam-587 36 10 the the DET ejpam-587 36 11 mentioned mention VERB ejpam-587 36 12 researchers researcher NOUN ejpam-587 36 13 above above ADV ejpam-587 36 14 are be AUX ejpam-587 36 15 studied study VERB ejpam-587 36 16 the the DET ejpam-587 36 17 bochner bochner NOUN ejpam-587 36 18 tensor tensor NOUN ejpam-587 36 19 on on ADP ejpam-587 36 20 some some DET ejpam-587 36 21 kinds kind NOUN ejpam-587 36 22 of of ADP ejpam-587 36 23 the the DET ejpam-587 36 24 sixteen sixteen NUM ejpam-587 36 25 classes class NOUN ejpam-587 36 26 of of ADP ejpam-587 36 27 almost almost ADV ejpam-587 36 28 hermitian hermitian ADJ ejpam-587 36 29 manifold manifold NOUN ejpam-587 36 30 . . PUNCT ejpam-587 37 1 in in ADP ejpam-587 37 2 the the DET ejpam-587 37 3 present present ADJ ejpam-587 37 4 paper paper NOUN ejpam-587 37 5 we we PRON ejpam-587 37 6 study study VERB ejpam-587 37 7 the the DET ejpam-587 37 8 flat flat ADJ ejpam-587 37 9 bochner bochner NOUN ejpam-587 37 10 tensor tensor NOUN ejpam-587 37 11 on on ADP ejpam-587 37 12 general general ADJ ejpam-587 37 13 class class NOUN ejpam-587 37 14 almost almost ADV ejpam-587 37 15 hermitian hermitian ADJ ejpam-587 37 16 manifold manifold NOUN ejpam-587 37 17 . . PUNCT ejpam-587 38 1 this this DET ejpam-587 38 2 study study NOUN ejpam-587 38 3 uses use VERB ejpam-587 38 4 the the DET ejpam-587 38 5 method method NOUN ejpam-587 38 6 of of ADP ejpam-587 38 7 adjoint adjoint PROPN ejpam-587 38 8 g g NOUN ejpam-587 38 9 - - PUNCT ejpam-587 38 10 structure structure NOUN ejpam-587 38 11 space space NOUN ejpam-587 38 12 which which PRON ejpam-587 38 13 was be AUX ejpam-587 38 14 introduced introduce VERB ejpam-587 38 15 by by ADP ejpam-587 38 16 v.f v.f PROPN ejpam-587 38 17 . . PROPN ejpam-587 38 18 krichenko krichenko PROPN ejpam-587 38 19 who who PRON ejpam-587 38 20 found find VERB ejpam-587 38 21 two two NUM ejpam-587 38 22 tensors tensor NOUN ejpam-587 38 23 which which PRON ejpam-587 38 24 are be AUX ejpam-587 38 25 the the DET ejpam-587 38 26 structure structure NOUN ejpam-587 38 27 and and CCONJ ejpam-587 38 28 virtual virtual ADJ ejpam-587 38 29 tensors tensor NOUN ejpam-587 38 30 [ [ X ejpam-587 38 31 5 5 NUM ejpam-587 38 32 ] ] PUNCT ejpam-587 38 33 . . PUNCT ejpam-587 39 1 this this DET ejpam-587 39 2 method method NOUN ejpam-587 39 3 helped help VERB ejpam-587 39 4 the the DET ejpam-587 39 5 researchers researcher NOUN ejpam-587 39 6 to to PART ejpam-587 39 7 study study VERB ejpam-587 39 8 the the DET ejpam-587 39 9 different different ADJ ejpam-587 39 10 geometrical geometrical ADJ ejpam-587 39 11 properties property NOUN ejpam-587 39 12 of of ADP ejpam-587 39 13 almost almost ADV ejpam-587 39 14 hermitian hermitian ADJ ejpam-587 39 15 manifold manifold NOUN ejpam-587 39 16 , , PUNCT ejpam-587 39 17 therefore therefore ADV ejpam-587 39 18 we we PRON ejpam-587 39 19 use use VERB ejpam-587 39 20 this this DET ejpam-587 39 21 method method NOUN ejpam-587 39 22 to to PART ejpam-587 39 23 generalize generalize VERB ejpam-587 39 24 the the DET ejpam-587 39 25 results result NOUN ejpam-587 39 26 which which PRON ejpam-587 39 27 are be AUX ejpam-587 39 28 given give VERB ejpam-587 39 29 by by ADP ejpam-587 39 30 vanhecke vanhecke NOUN ejpam-587 39 31 and and CCONJ ejpam-587 39 32 by by ADP ejpam-587 39 33 the the DET ejpam-587 39 34 referred refer VERB ejpam-587 39 35 researchers researcher NOUN ejpam-587 39 36 . . PUNCT ejpam-587 40 1 2 2 X ejpam-587 40 2 . . X ejpam-587 40 3 preliminaries preliminary NOUN ejpam-587 40 4 let let VERB ejpam-587 40 5 m m PRON ejpam-587 40 6 be be AUX ejpam-587 40 7 2n 2n NUM ejpam-587 40 8 - - PUNCT ejpam-587 40 9 dimensional dimensional ADJ ejpam-587 40 10 smooth smooth ADJ ejpam-587 40 11 manifold manifold NOUN ejpam-587 40 12 , , PUNCT ejpam-587 40 13 x x X ejpam-587 40 14 ( ( PUNCT ejpam-587 40 15 m m NOUN ejpam-587 40 16 ) ) PUNCT ejpam-587 40 17 be be AUX ejpam-587 40 18 a a DET ejpam-587 40 19 module module NOUN ejpam-587 40 20 of of ADP ejpam-587 40 21 smooth smooth ADJ ejpam-587 40 22 vector vector NOUN ejpam-587 40 23 fields field NOUN ejpam-587 40 24 on on ADP ejpam-587 40 25 m m NOUN ejpam-587 40 26 and and CCONJ ejpam-587 40 27 c∞(m c∞(m NOUN ejpam-587 40 28 ) ) PUNCT ejpam-587 40 29 be be AUX ejpam-587 40 30 an an DET ejpam-587 40 31 algebra algebra NOUN ejpam-587 40 32 of of ADP ejpam-587 40 33 smooth smooth ADJ ejpam-587 40 34 functions function NOUN ejpam-587 40 35 on on ADP ejpam-587 40 36 m m PROPN ejpam-587 40 37 . . PUNCT ejpam-587 41 1 an an DET ejpam-587 41 2 almost almost ADV ejpam-587 41 3 hermitian hermitian ADJ ejpam-587 41 4 structure structure NOUN ejpam-587 41 5 ( ( PUNCT ejpam-587 41 6 ah ah INTJ ejpam-587 41 7 - - PUNCT ejpam-587 41 8 structure structure NOUN ejpam-587 41 9 ) ) PUNCT ejpam-587 41 10 on on ADP ejpam-587 41 11 m m PROPN ejpam-587 41 12 is be AUX ejpam-587 41 13 a a DET ejpam-587 41 14 pair pair NOUN ejpam-587 41 15 � � PROPN ejpam-587 41 16 j j PROPN ejpam-587 41 17 , , PUNCT ejpam-587 41 18 g g PROPN ejpam-587 41 19 = = PROPN ejpam-587 41 20 < < X ejpam-587 41 21 . . PUNCT ejpam-587 41 22 , , PUNCT ejpam-587 41 23 . . PUNCT ejpam-587 42 1 > > X ejpam-587 42 2 , , PUNCT ejpam-587 42 3 where where SCONJ ejpam-587 42 4 j j PROPN ejpam-587 42 5 is be AUX ejpam-587 42 6 an an DET ejpam-587 42 7 endomorphism endomorphism NOUN ejpam-587 42 8 of of ADP ejpam-587 42 9 a a DET ejpam-587 42 10 tangent tangent ADJ ejpam-587 42 11 space space NOUN ejpam-587 42 12 tp(m tp(m PUNCT ejpam-587 42 13 ) ) PUNCT ejpam-587 43 1 with with ADP ejpam-587 43 2 � � PROPN ejpam-587 43 3 jp jp NOUN ejpam-587 43 4 � � PROPN ejpam-587 43 5 2 2 NUM ejpam-587 43 6 = = SYM ejpam-587 43 7 −id −id NOUN ejpam-587 43 8 and and CCONJ ejpam-587 43 9 g g NOUN ejpam-587 43 10 is be AUX ejpam-587 43 11 a a DET ejpam-587 43 12 reimannian reimannian ADJ ejpam-587 43 13 metric metric NOUN ejpam-587 43 14 on on ADP ejpam-587 43 15 m m PRON ejpam-587 43 16 such such ADJ ejpam-587 43 17 that that SCONJ ejpam-587 43 18 < < X ejpam-587 43 19 jx jx PROPN ejpam-587 43 20 , , PUNCT ejpam-587 43 21 jy jy PROPN ejpam-587 43 22 > > PUNCT ejpam-587 43 23 = = X ejpam-587 43 24 < < X ejpam-587 43 25 x x X ejpam-587 43 26 , , PUNCT ejpam-587 43 27 y y PROPN ejpam-587 43 28 > > X ejpam-587 43 29 , , PUNCT ejpam-587 43 30 x x X ejpam-587 43 31 , , PUNCT ejpam-587 43 32 y y PROPN ejpam-587 43 33 ∈ ∈ PROPN ejpam-587 43 34 x x SYM ejpam-587 43 35 ( ( PUNCT ejpam-587 43 36 m m NOUN ejpam-587 43 37 ) ) PUNCT ejpam-587 43 38 . . PUNCT ejpam-587 44 1 a a DET ejpam-587 44 2 smooth smooth ADJ ejpam-587 44 3 manifold manifold NOUN ejpam-587 44 4 provided provide VERB ejpam-587 44 5 ah ah INTJ ejpam-587 44 6 - - PUNCT ejpam-587 44 7 structure structure NOUN ejpam-587 45 1 is be AUX ejpam-587 45 2 called call VERB ejpam-587 45 3 an an DET ejpam-587 45 4 almost almost ADV ejpam-587 45 5 hermitian hermitian ADJ ejpam-587 45 6 manifold(ah manifold(ah NOUN ejpam-587 45 7 - - PUNCT ejpam-587 45 8 manifold manifold NOUN ejpam-587 45 9 ) ) PUNCT ejpam-587 45 10 . . PUNCT ejpam-587 46 1 we we PRON ejpam-587 46 2 recall recall VERB ejpam-587 46 3 that that SCONJ ejpam-587 46 4 the the DET ejpam-587 46 5 fundamental fundamental ADJ ejpam-587 46 6 ( ( PUNCT ejpam-587 46 7 kahlerian kahlerian NOUN ejpam-587 46 8 [ [ X ejpam-587 46 9 7 7 NUM ejpam-587 46 10 ] ] PUNCT ejpam-587 46 11 ) ) PUNCT ejpam-587 46 12 form form NOUN ejpam-587 46 13 is be AUX ejpam-587 46 14 given give VERB ejpam-587 46 15 by by ADP ejpam-587 46 16 ω(x ω(x X ejpam-587 46 17 , , PUNCT ejpam-587 46 18 y y PROPN ejpam-587 46 19 ) ) PUNCT ejpam-587 47 1 = = NOUN ejpam-587 47 2 < < X ejpam-587 47 3 x x X ejpam-587 47 4 , , PUNCT ejpam-587 47 5 jy jy PROPN ejpam-587 47 6 > > X ejpam-587 47 7 . . PUNCT ejpam-587 48 1 as as SCONJ ejpam-587 48 2 it it PRON ejpam-587 48 3 is be AUX ejpam-587 48 4 well well ADV ejpam-587 48 5 known know VERB ejpam-587 48 6 from from ADP ejpam-587 48 7 [ [ X ejpam-587 48 8 6 6 NUM ejpam-587 48 9 ] ] PUNCT ejpam-587 48 10 that that SCONJ ejpam-587 48 11 the the DET ejpam-587 48 12 given give VERB ejpam-587 48 13 ah ah INTJ ejpam-587 48 14 - - PUNCT ejpam-587 48 15 structure structure NOUN ejpam-587 48 16 on on ADP ejpam-587 48 17 a a DET ejpam-587 48 18 manifold manifold ADJ ejpam-587 48 19 m m NOUN ejpam-587 48 20 is be AUX ejpam-587 48 21 equivalent equivalent ADJ ejpam-587 48 22 to to ADP ejpam-587 48 23 the the DET ejpam-587 48 24 given give VERB ejpam-587 48 25 an an DET ejpam-587 48 26 g g NOUN ejpam-587 48 27 - - PUNCT ejpam-587 48 28 structure structure NOUN ejpam-587 48 29 in in ADP ejpam-587 48 30 principle principle ADJ ejpam-587 48 31 fiber fiber NOUN ejpam-587 48 32 bundle bundle NOUN ejpam-587 48 33 of of ADP ejpam-587 48 34 all all DET ejpam-587 48 35 complex complex ADJ ejpam-587 48 36 frames frame NOUN ejpam-587 48 37 of of ADP ejpam-587 48 38 m m PROPN ejpam-587 48 39 with with ADP ejpam-587 48 40 structure structure NOUN ejpam-587 48 41 group group NOUN ejpam-587 48 42 u(n u(n PROPN ejpam-587 48 43 ) ) PUNCT ejpam-587 48 44 . . PUNCT ejpam-587 49 1 this this DET ejpam-587 49 2 group group NOUN ejpam-587 49 3 is be AUX ejpam-587 49 4 called call VERB ejpam-587 49 5 an an DET ejpam-587 49 6 adjoint adjoint NOUN ejpam-587 49 7 g g NOUN ejpam-587 49 8 - - NOUN ejpam-587 49 9 structure structure NOUN ejpam-587 49 10 . . PUNCT ejpam-587 50 1 the the DET ejpam-587 50 2 frame frame NOUN ejpam-587 50 3 adapted adapt VERB ejpam-587 50 4 to to ADP ejpam-587 50 5 the the DET ejpam-587 50 6 ahstructure ahstructure NOUN ejpam-587 50 7 is be AUX ejpam-587 50 8 called call VERB ejpam-587 50 9 a a DET ejpam-587 50 10 - - PUNCT ejpam-587 50 11 frame frame NOUN ejpam-587 50 12 look look NOUN ejpam-587 50 13 as as ADP ejpam-587 50 14 � � PROPN ejpam-587 50 15 p p PROPN ejpam-587 50 16 , , PUNCT ejpam-587 50 17 ǫ1 ǫ1 NOUN ejpam-587 50 18 , , PUNCT ejpam-587 50 19 . . PUNCT ejpam-587 50 20 . . PUNCT ejpam-587 51 1 . . PUNCT ejpam-587 52 1 , , PUNCT ejpam-587 52 2 ǫn ǫn X ejpam-587 52 3 , , PUNCT ejpam-587 52 4 ǫ1̂ ǫ1̂ NUM ejpam-587 52 5 , , PUNCT ejpam-587 52 6 . . PUNCT ejpam-587 52 7 . . PUNCT ejpam-587 52 8 . . PUNCT ejpam-587 53 1 , , PUNCT ejpam-587 54 1 ǫn̂ ǫn̂ NUM ejpam-587 54 2 [ [ X ejpam-587 54 3 5 5 NUM ejpam-587 54 4 ] ] PUNCT ejpam-587 54 5 , , PUNCT ejpam-587 54 6 where where SCONJ ejpam-587 54 7 ǫa ǫa PRON ejpam-587 54 8 are be AUX ejpam-587 54 9 the the DET ejpam-587 54 10 eigenvectors eigenvector NOUN ejpam-587 54 11 corresponded correspond VERB ejpam-587 54 12 to to ADP ejpam-587 54 13 the the DET ejpam-587 54 14 eigenvalue eigenvalue PROPN ejpam-587 54 15 i i PROPN ejpam-587 54 16 = = SYM ejpam-587 54 17 p−1 p−1 PROPN ejpam-587 54 18 and and CCONJ ejpam-587 54 19 ǫâ ǫâ PROPN ejpam-587 54 20 are be AUX ejpam-587 54 21 the the DET ejpam-587 54 22 eigenvectors eigenvector NOUN ejpam-587 54 23 corresponded correspond VERB ejpam-587 54 24 to to ADP ejpam-587 54 25 the the DET ejpam-587 54 26 eigenvalue eigenvalue PROPN ejpam-587 54 27 i i NOUN ejpam-587 54 28 = = NOUN ejpam-587 54 29 −p−1 −p−1 NUM ejpam-587 54 30 . . PUNCT ejpam-587 55 1 here here ADV ejpam-587 55 2 the the DET ejpam-587 55 3 index index NOUN ejpam-587 55 4 a a DET ejpam-587 55 5 ranges range NOUN ejpam-587 55 6 from from ADP ejpam-587 55 7 1 1 NUM ejpam-587 55 8 to to ADP ejpam-587 55 9 n n PROPN ejpam-587 55 10 and and CCONJ ejpam-587 55 11 â â X ejpam-587 55 12 = = PRON ejpam-587 55 13 a+ a+ PUNCT ejpam-587 55 14 n. n. NOUN ejpam-587 55 15 the the DET ejpam-587 55 16 matrices matrix NOUN ejpam-587 55 17 of of ADP ejpam-587 55 18 the the DET ejpam-587 55 19 j j PROPN ejpam-587 55 20 , , PUNCT ejpam-587 55 21 g g PROPN ejpam-587 55 22 and and CCONJ ejpam-587 55 23 ω ω PROPN ejpam-587 55 24 in in ADP ejpam-587 55 25 a a DET ejpam-587 55 26 - - PUNCT ejpam-587 55 27 frame frame NOUN ejpam-587 55 28 are be AUX ejpam-587 55 29 given give VERB ejpam-587 55 30 as as ADP ejpam-587 55 31 : : PUNCT ejpam-587 55 32 � � PROPN ejpam-587 55 33 gi gi PROPN ejpam-587 55 34 j j PROPN ejpam-587 55 35 � � PROPN ejpam-587 55 36 = = SYM ejpam-587 55 37 � � PROPN ejpam-587 55 38 0 0 NUM ejpam-587 55 39 in in ADP ejpam-587 55 40 in in ADP ejpam-587 55 41 0 0 NUM ejpam-587 55 42 � � PROPN ejpam-587 55 43 , , PUNCT ejpam-587 55 44 � � PROPN ejpam-587 55 45 j j PROPN ejpam-587 56 1 i i PROPN ejpam-587 56 2 j j PROPN ejpam-587 56 3 � � PROPN ejpam-587 56 4 = = SYM ejpam-587 56 5 � � PROPN ejpam-587 56 6 p−1jn p−1jn NOUN ejpam-587 56 7 0 0 NUM ejpam-587 56 8 0 0 NUM ejpam-587 56 9 −p−1jn −p−1jn NOUN ejpam-587 56 10 � � PROPN ejpam-587 56 11 , , PUNCT ejpam-587 56 12 ( ( PUNCT ejpam-587 56 13 ωi ωi PROPN ejpam-587 56 14 j j NOUN ejpam-587 56 15 ) ) PUNCT ejpam-587 56 16 = = SYM ejpam-587 56 17 � � PROPN ejpam-587 56 18 0 0 NUM ejpam-587 56 19 p−1 p−1 PROPN ejpam-587 56 20 in in ADP ejpam-587 56 21 −p−1 −p−1 NUM ejpam-587 56 22 in in ADP ejpam-587 56 23 0 0 NUM ejpam-587 56 24 � � PROPN ejpam-587 56 25 ( ( PUNCT ejpam-587 56 26 1 1 NUM ejpam-587 56 27 ) ) PUNCT ejpam-587 56 28 where where SCONJ ejpam-587 56 29 in in ADP ejpam-587 56 30 is be AUX ejpam-587 56 31 the the DET ejpam-587 56 32 identity identity NOUN ejpam-587 56 33 matrix matrix NOUN ejpam-587 56 34 of of ADP ejpam-587 56 35 order order NOUN ejpam-587 56 36 n. n. VERB ejpam-587 56 37 a a DET ejpam-587 56 38 bochner bochner NOUN ejpam-587 56 39 tensor tensor NOUN ejpam-587 56 40 on on ADP ejpam-587 56 41 ah ah INTJ ejpam-587 56 42 - - PUNCT ejpam-587 56 43 manifold manifold ADJ ejpam-587 56 44 m m NOUN ejpam-587 56 45 is be AUX ejpam-587 56 46 a a DET ejpam-587 56 47 tensor tensor NOUN ejpam-587 56 48 of of ADP ejpam-587 56 49 type type NOUN ejpam-587 56 50 ( ( PUNCT ejpam-587 56 51 4,0 4,0 NUM ejpam-587 56 52 ) ) PUNCT ejpam-587 56 53 which which PRON ejpam-587 56 54 is be AUX ejpam-587 56 55 defined define VERB ejpam-587 56 56 as as ADP ejpam-587 56 57 the the DET ejpam-587 56 58 form form NOUN ejpam-587 56 59 : : PUNCT ejpam-587 56 60 b(x b(x NOUN ejpam-587 56 61 , , PUNCT ejpam-587 56 62 y y PROPN ejpam-587 56 63 , , PUNCT ejpam-587 56 64 z z NOUN ejpam-587 56 65 , , PUNCT ejpam-587 56 66 w w PROPN ejpam-587 56 67 ) ) PUNCT ejpam-587 57 1 = = SYM ejpam-587 57 2 r(x r(x PROPN ejpam-587 57 3 , , PUNCT ejpam-587 57 4 y y PROPN ejpam-587 57 5 , , PUNCT ejpam-587 57 6 z z NOUN ejpam-587 57 7 , , PUNCT ejpam-587 57 8 w w PROPN ejpam-587 57 9 ) ) PUNCT ejpam-587 58 1 + + CCONJ ejpam-587 58 2 l(x l(x PROPN ejpam-587 58 3 , , PUNCT ejpam-587 58 4 w w NOUN ejpam-587 58 5 ) ) PUNCT ejpam-587 58 6 g(y g(y PROPN ejpam-587 58 7 , , PUNCT ejpam-587 58 8 z)− z)− PROPN ejpam-587 58 9 l(x l(x PROPN ejpam-587 58 10 , , PUNCT ejpam-587 58 11 z)g(y z)g(y PROPN ejpam-587 58 12 , , PUNCT ejpam-587 58 13 w w NOUN ejpam-587 58 14 ) ) PUNCT ejpam-587 59 1 + + CCONJ ejpam-587 60 1 l(y l(y PROPN ejpam-587 60 2 , , PUNCT ejpam-587 60 3 z)g(x z)g(x NUM ejpam-587 60 4 , , PUNCT ejpam-587 60 5 w w NOUN ejpam-587 60 6 ) ) PUNCT ejpam-587 60 7 − − PROPN ejpam-587 61 1 l(y l(y PROPN ejpam-587 61 2 , , PUNCT ejpam-587 61 3 w w NOUN ejpam-587 61 4 ) ) PUNCT ejpam-587 61 5 g(x g(x NOUN ejpam-587 61 6 , , PUNCT ejpam-587 61 7 z z NOUN ejpam-587 61 8 ) ) PUNCT ejpam-587 62 1 + + CCONJ ejpam-587 62 2 l(jx l(jx PROPN ejpam-587 62 3 , , PUNCT ejpam-587 62 4 w w NOUN ejpam-587 62 5 ) ) PUNCT ejpam-587 62 6 g(jx g(jx PROPN ejpam-587 62 7 , , PUNCT ejpam-587 62 8 z z NOUN ejpam-587 62 9 ) ) PUNCT ejpam-587 62 10 − − ADP ejpam-587 62 11 l(jx l(jx PROPN ejpam-587 62 12 , , PUNCT ejpam-587 62 13 z)g(jy z)g(jy PROPN ejpam-587 62 14 , , PUNCT ejpam-587 62 15 w w NOUN ejpam-587 62 16 ) ) PUNCT ejpam-587 63 1 + + CCONJ ejpam-587 63 2 l(jy l(jy ADJ ejpam-587 63 3 , , PUNCT ejpam-587 63 4 z)g(jx z)g(jx PUNCT ejpam-587 63 5 , , PUNCT ejpam-587 63 6 w w PROPN ejpam-587 63 7 ) ) PUNCT ejpam-587 64 1 − − PROPN ejpam-587 64 2 l(jy l(jy PROPN ejpam-587 64 3 , , PUNCT ejpam-587 64 4 w w NOUN ejpam-587 64 5 ) ) PUNCT ejpam-587 64 6 g(jx g(jx PROPN ejpam-587 64 7 , , PUNCT ejpam-587 64 8 z z NOUN ejpam-587 64 9 ) ) PUNCT ejpam-587 64 10 − − PROPN ejpam-587 64 11 2l(jx 2l(jx NUM ejpam-587 64 12 , , PUNCT ejpam-587 64 13 y y PROPN ejpam-587 64 14 ) ) PUNCT ejpam-587 65 1 g(j g(j PROPN ejpam-587 65 2 z z PROPN ejpam-587 65 3 , , PUNCT ejpam-587 65 4 w w PROPN ejpam-587 65 5 ) ) PUNCT ejpam-587 65 6 − − PROPN ejpam-587 65 7 2l(j 2l(j PROPN ejpam-587 65 8 z z NOUN ejpam-587 65 9 , , PUNCT ejpam-587 65 10 w w NOUN ejpam-587 65 11 ) ) PUNCT ejpam-587 65 12 g(jx g(jx PROPN ejpam-587 65 13 , , PUNCT ejpam-587 65 14 y y PROPN ejpam-587 65 15 ) ) PUNCT ejpam-587 65 16 , , PUNCT ejpam-587 65 17 where where SCONJ ejpam-587 65 18 l l NOUN ejpam-587 65 19 ( ( PUNCT ejpam-587 65 20 x x INTJ ejpam-587 65 21 , , PUNCT ejpam-587 65 22 y y PROPN ejpam-587 65 23 ) ) PUNCT ejpam-587 65 24 = = PUNCT ejpam-587 66 1 − − PROPN ejpam-587 66 2 1 1 NUM ejpam-587 66 3 2n+ 2n+ NUM ejpam-587 66 4 4 4 NUM ejpam-587 66 5 g g NOUN ejpam-587 66 6 ( ( PUNCT ejpam-587 66 7 rx rx NOUN ejpam-587 66 8 , , PUNCT ejpam-587 66 9 y y PROPN ejpam-587 66 10 ) ) PUNCT ejpam-587 67 1 + + CCONJ ejpam-587 68 1 k k PROPN ejpam-587 68 2 2 2 NUM ejpam-587 68 3 ( ( PUNCT ejpam-587 68 4 2n+ 2n+ NUM ejpam-587 68 5 2 2 NUM ejpam-587 68 6 ) ) PUNCT ejpam-587 68 7 ( ( PUNCT ejpam-587 68 8 2n+ 2n+ NUM ejpam-587 68 9 4 4 NUM ejpam-587 68 10 ) ) PUNCT ejpam-587 68 11 g g NOUN ejpam-587 68 12 ( ( PUNCT ejpam-587 68 13 x x PROPN ejpam-587 68 14 , , PUNCT ejpam-587 68 15 y y PROPN ejpam-587 68 16 ) ) PUNCT ejpam-587 68 17 , , PUNCT ejpam-587 68 18 h. h. PROPN ejpam-587 68 19 abood abood PROPN ejpam-587 68 20 / / SYM ejpam-587 68 21 eur eur PROPN ejpam-587 68 22 . . PUNCT ejpam-587 69 1 j. j. PROPN ejpam-587 69 2 pure pure PROPN ejpam-587 69 3 appl appl PROPN ejpam-587 69 4 . . PROPN ejpam-587 69 5 math math PROPN ejpam-587 69 6 , , PUNCT ejpam-587 69 7 3 3 NUM ejpam-587 69 8 ( ( PUNCT ejpam-587 69 9 2010 2010 NUM ejpam-587 69 10 ) ) PUNCT ejpam-587 69 11 , , PUNCT ejpam-587 69 12 730 730 NUM ejpam-587 69 13 - - SYM ejpam-587 69 14 736 736 NUM ejpam-587 69 15 732 732 NUM ejpam-587 69 16 r r NOUN ejpam-587 69 17 is be AUX ejpam-587 69 18 the the DET ejpam-587 69 19 ricci ricci PROPN ejpam-587 69 20 tensor tensor NOUN ejpam-587 69 21 and and CCONJ ejpam-587 69 22 k k PROPN ejpam-587 69 23 is be AUX ejpam-587 69 24 the the DET ejpam-587 69 25 scalar scalar ADJ ejpam-587 69 26 curvature curvature NOUN ejpam-587 69 27 tensor tensor NOUN ejpam-587 69 28 , , PUNCT ejpam-587 69 29 x x NOUN ejpam-587 69 30 , , PUNCT ejpam-587 69 31 y y PROPN ejpam-587 69 32 , , PUNCT ejpam-587 69 33 z z NOUN ejpam-587 69 34 , , PUNCT ejpam-587 69 35 w w PROPN ejpam-587 69 36 ∈ ∈ PROPN ejpam-587 69 37 x x SYM ejpam-587 69 38 ( ( PUNCT ejpam-587 69 39 m m NOUN ejpam-587 69 40 ) ) PUNCT ejpam-587 69 41 . . PUNCT ejpam-587 70 1 denote denote PROPN ejpam-587 70 2 c c NOUN ejpam-587 70 3 ( ( PUNCT ejpam-587 70 4 x x INTJ ejpam-587 70 5 , , PUNCT ejpam-587 70 6 y y PROPN ejpam-587 70 7 ) ) PUNCT ejpam-587 71 1 = = X ejpam-587 71 2 l l NOUN ejpam-587 71 3 ( ( PUNCT ejpam-587 71 4 jx jx PROPN ejpam-587 71 5 , , PUNCT ejpam-587 71 6 y y PROPN ejpam-587 71 7 ) ) PUNCT ejpam-587 71 8 . . PUNCT ejpam-587 72 1 we we PRON ejpam-587 72 2 have have VERB ejpam-587 72 3 g g PROPN ejpam-587 72 4 ( ( PUNCT ejpam-587 72 5 jx jx PROPN ejpam-587 72 6 , , PUNCT ejpam-587 72 7 y y PROPN ejpam-587 72 8 ) ) PUNCT ejpam-587 72 9 = = PUNCT ejpam-587 73 1 −ω(x −ω(x X ejpam-587 73 2 , , PUNCT ejpam-587 73 3 y y PROPN ejpam-587 73 4 ) ) PUNCT ejpam-587 73 5 , , PUNCT ejpam-587 73 6 where where SCONJ ejpam-587 73 7 ω ω PROPN ejpam-587 73 8 is be AUX ejpam-587 73 9 the the DET ejpam-587 73 10 fundamental(kahlerian fundamental(kahlerian ADJ ejpam-587 73 11 ) ) PUNCT ejpam-587 73 12 form form NOUN ejpam-587 73 13 . . PUNCT ejpam-587 74 1 the the DET ejpam-587 74 2 components component NOUN ejpam-587 74 3 of of ADP ejpam-587 74 4 bochner bochner NOUN ejpam-587 74 5 tensor tensor NOUN ejpam-587 74 6 at at ADP ejpam-587 74 7 any any DET ejpam-587 74 8 frame frame NOUN ejpam-587 74 9 will will AUX ejpam-587 74 10 be be AUX ejpam-587 74 11 as as ADP ejpam-587 74 12 the the DET ejpam-587 74 13 form form NOUN ejpam-587 74 14 : : PUNCT ejpam-587 74 15 bi bi PROPN ejpam-587 74 16 jkl jkl PROPN ejpam-587 74 17 = = SYM ejpam-587 74 18 ri ri PROPN ejpam-587 74 19 jkl jkl NOUN ejpam-587 74 20 + + CCONJ ejpam-587 74 21 lil lil VERB ejpam-587 74 22 g g PROPN ejpam-587 74 23 jk jk PROPN ejpam-587 74 24 − − PROPN ejpam-587 74 25 lik lik VERB ejpam-587 74 26 g g PROPN ejpam-587 74 27 jl jl PROPN ejpam-587 74 28 + + CCONJ ejpam-587 74 29 l l PROPN ejpam-587 74 30 jk jk PROPN ejpam-587 74 31 gil gil PROPN ejpam-587 75 1 − − PROPN ejpam-587 75 2 l l NOUN ejpam-587 75 3 jl jl NOUN ejpam-587 75 4 gik gik NOUN ejpam-587 75 5 − − PROPN ejpam-587 75 6 cilω cilω PROPN ejpam-587 75 7 jk jk PROPN ejpam-587 75 8 + + CCONJ ejpam-587 75 9 cikω cikω NOUN ejpam-587 75 10 jl jl NOUN ejpam-587 75 11 − − PROPN ejpam-587 75 12 c c NOUN ejpam-587 75 13 jkωil jkωil NOUN ejpam-587 75 14 + + CCONJ ejpam-587 75 15 c c PROPN ejpam-587 75 16 jlωik jlωik NOUN ejpam-587 75 17 + + CCONJ ejpam-587 75 18 2ci 2ci ADJ ejpam-587 75 19 jωkl jωkl NOUN ejpam-587 75 20 + + CCONJ ejpam-587 75 21 2cklωi 2cklωi NUM ejpam-587 75 22 j j PROPN ejpam-587 75 23 ( ( PUNCT ejpam-587 75 24 2 2 NUM ejpam-587 75 25 ) ) PUNCT ejpam-587 75 26 li li PROPN ejpam-587 75 27 j j PROPN ejpam-587 75 28 = = SYM ejpam-587 76 1 − − PROPN ejpam-587 76 2 1 1 NUM ejpam-587 76 3 2n+ 2n+ NUM ejpam-587 76 4 4 4 NUM ejpam-587 76 5 ri ri PROPN ejpam-587 76 6 j j PROPN ejpam-587 76 7 + + CCONJ ejpam-587 77 1 k̃ k̃ PROPN ejpam-587 77 2 gi gi PROPN ejpam-587 77 3 j j PROPN ejpam-587 77 4 ( ( PUNCT ejpam-587 77 5 3 3 NUM ejpam-587 77 6 ) ) PUNCT ejpam-587 77 7 ci ci PROPN ejpam-587 77 8 j j PROPN ejpam-587 77 9 = = SYM ejpam-587 78 1 − − PROPN ejpam-587 78 2 1 1 NUM ejpam-587 78 3 2n+ 2n+ NUM ejpam-587 78 4 4 4 NUM ejpam-587 78 5 j j NOUN ejpam-587 79 1 k k NOUN ejpam-587 80 1 i i PRON ejpam-587 80 2 rk rk VERB ejpam-587 80 3 j j NOUN ejpam-587 81 1 + + CCONJ ejpam-587 81 2 k̃j k̃j PROPN ejpam-587 82 1 k k INTJ ejpam-587 83 1 i i PRON ejpam-587 83 2 gk gk PROPN ejpam-587 83 3 j j PROPN ejpam-587 83 4 ( ( PUNCT ejpam-587 83 5 4 4 NUM ejpam-587 83 6 ) ) PUNCT ejpam-587 83 7 where where SCONJ ejpam-587 83 8 k̃ k̃ PROPN ejpam-587 83 9 = = SYM ejpam-587 83 10 k k PROPN ejpam-587 83 11 2 2 NUM ejpam-587 83 12 ( ( PUNCT ejpam-587 83 13 2n+ 2n+ NUM ejpam-587 83 14 2 2 NUM ejpam-587 83 15 ) ) PUNCT ejpam-587 83 16 ( ( PUNCT ejpam-587 83 17 2n+ 2n+ NUM ejpam-587 83 18 4 4 NUM ejpam-587 83 19 ) ) PUNCT ejpam-587 83 20 suppose suppose VERB ejpam-587 83 21 that that SCONJ ejpam-587 83 22 the the DET ejpam-587 83 23 indices index NOUN ejpam-587 83 24 a a DET ejpam-587 83 25 , , PUNCT ejpam-587 83 26 b b NOUN ejpam-587 83 27 , , PUNCT ejpam-587 83 28 c c PROPN ejpam-587 83 29 and and CCONJ ejpam-587 83 30 d d PROPN ejpam-587 83 31 in in ADP ejpam-587 83 32 the the DET ejpam-587 83 33 range range NOUN ejpam-587 83 34 1,2 1,2 NUM ejpam-587 83 35 , , PUNCT ejpam-587 83 36 . . PUNCT ejpam-587 83 37 . . PUNCT ejpam-587 84 1 . . PUNCT ejpam-587 85 1 , , PUNCT ejpam-587 85 2 n. n. PROPN ejpam-587 85 3 denote denote VERB ejpam-587 85 4 â â PROPN ejpam-587 85 5 = = PRON ejpam-587 85 6 a+ a+ PUNCT ejpam-587 85 7 n. n. NOUN ejpam-587 85 8 in in ADP ejpam-587 85 9 the the DET ejpam-587 85 10 following follow VERB ejpam-587 85 11 proposition proposition NOUN ejpam-587 85 12 we we PRON ejpam-587 85 13 find find VERB ejpam-587 85 14 the the DET ejpam-587 85 15 components component NOUN ejpam-587 85 16 of of ADP ejpam-587 85 17 bochner bochner NOUN ejpam-587 85 18 tensor tensor NOUN ejpam-587 85 19 on on ADP ejpam-587 85 20 any any DET ejpam-587 85 21 ah ah INTJ ejpam-587 85 22 - - PUNCT ejpam-587 85 23 manifold manifold NOUN ejpam-587 85 24 in in ADP ejpam-587 85 25 the the DET ejpam-587 85 26 ajoint ajoint NOUN ejpam-587 85 27 g g NOUN ejpam-587 85 28 - - PUNCT ejpam-587 85 29 structure structure NOUN ejpam-587 85 30 space space NOUN ejpam-587 85 31 , , PUNCT ejpam-587 85 32 i.e. i.e. X ejpam-587 85 33 in in ADP ejpam-587 85 34 the the DET ejpam-587 85 35 a a DET ejpam-587 85 36 - - PUNCT ejpam-587 85 37 frame frame NOUN ejpam-587 85 38 : : PUNCT ejpam-587 85 39 proposition proposition NOUN ejpam-587 85 40 1 1 NUM ejpam-587 85 41 . . PUNCT ejpam-587 86 1 the the DET ejpam-587 86 2 components component NOUN ejpam-587 86 3 of of ADP ejpam-587 86 4 bochner bochner NOUN ejpam-587 86 5 tensor tensor NOUN ejpam-587 86 6 of of ADP ejpam-587 86 7 ah ah INTJ ejpam-587 86 8 - - PUNCT ejpam-587 86 9 manifold manifold NOUN ejpam-587 86 10 are be AUX ejpam-587 86 11 given give VERB ejpam-587 86 12 as as ADP ejpam-587 86 13 the the DET ejpam-587 86 14 following follow VERB ejpam-587 86 15 forms form NOUN ejpam-587 86 16 : : PUNCT ejpam-587 86 17 1 1 X ejpam-587 86 18 . . X ejpam-587 86 19 babcd babcd NOUN ejpam-587 86 20 = = PUNCT ejpam-587 86 21 rabcd rabcd VERB ejpam-587 86 22 2 2 NUM ejpam-587 86 23 . . PUNCT ejpam-587 86 24 bâbcd bâbcd PUNCT ejpam-587 86 25 = = PUNCT ejpam-587 86 26 râbcd râbcd PUNCT ejpam-587 86 27 + + CCONJ ejpam-587 86 28 1 1 NUM ejpam-587 86 29 n+2 n+2 NUM ejpam-587 86 30 ( ( PUNCT ejpam-587 86 31 rbdδ rbdδ VERB ejpam-587 86 32 a a DET ejpam-587 86 33 c c NOUN ejpam-587 86 34 − − NOUN ejpam-587 86 35 rbcδ rbcδ NOUN ejpam-587 87 1 a a DET ejpam-587 87 2 d d NOUN ejpam-587 87 3 + + CCONJ ejpam-587 87 4 rcdδ rcdδ VERB ejpam-587 87 5 a a DET ejpam-587 87 6 b b NOUN ejpam-587 87 7 ) ) PUNCT ejpam-587 87 8 3 3 NUM ejpam-587 87 9 . . X ejpam-587 87 10 bâ bâ PROPN ejpam-587 87 11 b̂cd b̂cd ADJ ejpam-587 87 12 = = SYM ejpam-587 87 13 râ râ X ejpam-587 87 14 b̂cd b̂cd NOUN ejpam-587 87 15 + + CCONJ ejpam-587 87 16 1 1 NUM ejpam-587 87 17 2n+4 2n+4 NUM ejpam-587 87 18 � � PROPN ejpam-587 88 1 ra ra PROPN ejpam-587 88 2 c c PROPN ejpam-587 88 3 δ δ PROPN ejpam-587 89 1 b b PROPN ejpam-587 89 2 d d NOUN ejpam-587 89 3 − − PROPN ejpam-587 89 4 ra ra PROPN ejpam-587 89 5 d d PROPN ejpam-587 89 6 δ δ PROPN ejpam-587 89 7 b b PROPN ejpam-587 89 8 c c PROPN ejpam-587 90 1 + + NOUN ejpam-587 90 2 r r NOUN ejpam-587 90 3 b b PROPN ejpam-587 90 4 d d PROPN ejpam-587 90 5 δ δ PROPN ejpam-587 90 6 a a DET ejpam-587 90 7 c c NOUN ejpam-587 91 1 − − NOUN ejpam-587 91 2 r r NOUN ejpam-587 91 3 b b PROPN ejpam-587 91 4 c c NOUN ejpam-587 91 5 δ δ PROPN ejpam-587 91 6 a a PROPN ejpam-587 91 7 d d X ejpam-587 91 8 � � PROPN ejpam-587 91 9 4 4 NUM ejpam-587 91 10 . . PUNCT ejpam-587 91 11 bâbcd̂ bâbcd̂ NOUN ejpam-587 91 12 = = PUNCT ejpam-587 91 13 râbcd̂ râbcd̂ NOUN ejpam-587 91 14 + + CCONJ ejpam-587 91 15 1 1 NUM ejpam-587 91 16 n+2 n+2 NUM ejpam-587 91 17 ( ( PUNCT ejpam-587 91 18 ra ra PROPN ejpam-587 91 19 b b PROPN ejpam-587 91 20 δ δ PROPN ejpam-587 91 21 d d PROPN ejpam-587 91 22 c c PROPN ejpam-587 91 23 − − PROPN ejpam-587 91 24 rd rd PROPN ejpam-587 91 25 c c PROPN ejpam-587 91 26 δ δ PROPN ejpam-587 91 27 a a DET ejpam-587 91 28 b b PROPN ejpam-587 91 29 ) ) PUNCT ejpam-587 91 30 5 5 NUM ejpam-587 91 31 . . PUNCT ejpam-587 92 1 bab̂cd bab̂cd PROPN ejpam-587 92 2 = = PUNCT ejpam-587 92 3 rab̂cd rab̂cd PROPN ejpam-587 92 4 − − NOUN ejpam-587 92 5 1 1 NUM ejpam-587 92 6 n+2 n+2 PRON ejpam-587 92 7 rcdδ rcdδ VERB ejpam-587 93 1 c c NOUN ejpam-587 93 2 d d NOUN ejpam-587 93 3 6 6 NUM ejpam-587 93 4 . . PUNCT ejpam-587 93 5 babĉd babĉd PART ejpam-587 93 6 = = SYM ejpam-587 93 7 rabĉd rabĉd NOUN ejpam-587 93 8 − − NOUN ejpam-587 93 9 1 1 NUM ejpam-587 93 10 n+2 n+2 PRON ejpam-587 93 11 rabδ rabδ VERB ejpam-587 93 12 c c PROPN ejpam-587 93 13 d d PROPN ejpam-587 93 14 7 7 NUM ejpam-587 93 15 . . PUNCT ejpam-587 93 16 babcd̂ babcd̂ PUNCT ejpam-587 94 1 = = SYM ejpam-587 94 2 rabcd̂ rabcd̂ NOUN ejpam-587 94 3 − − PROPN ejpam-587 94 4 1 1 NUM ejpam-587 94 5 n+2 n+2 PRON ejpam-587 94 6 rabδ rabδ VERB ejpam-587 94 7 d d PROPN ejpam-587 94 8 c c PROPN ejpam-587 94 9 8 8 NUM ejpam-587 94 10 . . PUNCT ejpam-587 94 11 bâbĉd bâbĉd PROPN ejpam-587 94 12 = = SYM ejpam-587 94 13 râbĉd râbĉd PROPN ejpam-587 94 14 + + SYM ejpam-587 94 15 1 1 NUM ejpam-587 94 16 n+2 n+2 NUM ejpam-587 94 17 � � PROPN ejpam-587 94 18 ra ra PROPN ejpam-587 94 19 b b PROPN ejpam-587 94 20 δ δ PROPN ejpam-587 94 21 c c PROPN ejpam-587 95 1 d d NOUN ejpam-587 95 2 + + CCONJ ejpam-587 95 3 r r NOUN ejpam-587 95 4 c c NOUN ejpam-587 95 5 d d NOUN ejpam-587 95 6 δ δ PROPN ejpam-587 95 7 a a PROPN ejpam-587 95 8 b b PROPN ejpam-587 95 9 � � PROPN ejpam-587 95 10 − − PROPN ejpam-587 95 11 4kδa 4kδa PROPN ejpam-587 95 12 b b PROPN ejpam-587 95 13 δ δ NOUN ejpam-587 95 14 c c NOUN ejpam-587 95 15 d d NOUN ejpam-587 95 16 and and CCONJ ejpam-587 95 17 the the DET ejpam-587 95 18 other other ADJ ejpam-587 95 19 components component NOUN ejpam-587 95 20 of of ADP ejpam-587 95 21 the the DET ejpam-587 95 22 bochner bochner NOUN ejpam-587 95 23 tensor tensor NOUN ejpam-587 95 24 are be AUX ejpam-587 95 25 conjugate conjugate ADJ ejpam-587 95 26 of of ADP ejpam-587 95 27 the the DET ejpam-587 95 28 above above ADJ ejpam-587 95 29 components component NOUN ejpam-587 95 30 . . PUNCT ejpam-587 96 1 proof proof NOUN ejpam-587 96 2 . . PUNCT ejpam-587 97 1 1 1 NUM ejpam-587 97 2 set set VERB ejpam-587 97 3 i i NOUN ejpam-587 97 4 = = SYM ejpam-587 97 5 a a X ejpam-587 97 6 , , PUNCT ejpam-587 97 7 j j PROPN ejpam-587 97 8 = = SYM ejpam-587 97 9 b b PROPN ejpam-587 97 10 , , PUNCT ejpam-587 97 11 k k PROPN ejpam-587 97 12 = = SYM ejpam-587 97 13 c c NOUN ejpam-587 97 14 , , PUNCT ejpam-587 97 15 l l NOUN ejpam-587 98 1 = = SYM ejpam-587 98 2 d d NOUN ejpam-587 98 3 , , PUNCT ejpam-587 98 4 thus thus ADV ejpam-587 98 5 equation equation NOUN ejpam-587 98 6 ( ( PUNCT ejpam-587 98 7 2 2 X ejpam-587 98 8 ) ) PUNCT ejpam-587 98 9 becomes become VERB ejpam-587 98 10 : : PUNCT ejpam-587 98 11 babcd babcd NOUN ejpam-587 98 12 = = PRON ejpam-587 98 13 rabcd rabcd VERB ejpam-587 98 14 + + CCONJ ejpam-587 98 15 lad lad ADJ ejpam-587 98 16 gbc gbc PROPN ejpam-587 98 17 − − PROPN ejpam-587 98 18 lac lac PROPN ejpam-587 98 19 gbd gbd PROPN ejpam-587 98 20 + + CCONJ ejpam-587 98 21 lbc lbc PROPN ejpam-587 98 22 gad gad PROPN ejpam-587 98 23 − − PROPN ejpam-587 98 24 lbd lbd PROPN ejpam-587 98 25 gac gac PROPN ejpam-587 98 26 − − PROPN ejpam-587 98 27 cadωbc+cacωbd−cbcωad cadωbc+cacωbd−cbcωad PROPN ejpam-587 99 1 + + CCONJ ejpam-587 99 2 cbdωac+2cabωcd cbdωac+2cabωcd NOUN ejpam-587 100 1 + + NOUN ejpam-587 100 2 2ccdωab 2ccdωab NUM ejpam-587 100 3 according accord VERB ejpam-587 100 4 to to ADP ejpam-587 100 5 equations equation NOUN ejpam-587 100 6 ( ( PUNCT ejpam-587 100 7 1 1 X ejpam-587 100 8 ) ) PUNCT ejpam-587 100 9 we we PRON ejpam-587 100 10 get get VERB ejpam-587 100 11 babcd babcd ADJ ejpam-587 100 12 = = NUM ejpam-587 100 13 rabcd rabcd ADV ejpam-587 100 14 . . PUNCT ejpam-587 101 1 h. h. PROPN ejpam-587 101 2 abood abood PROPN ejpam-587 101 3 / / SYM ejpam-587 101 4 eur eur PROPN ejpam-587 101 5 . . PUNCT ejpam-587 102 1 j. j. PROPN ejpam-587 102 2 pure pure PROPN ejpam-587 102 3 appl appl PROPN ejpam-587 102 4 . . PROPN ejpam-587 102 5 math math PROPN ejpam-587 102 6 , , PUNCT ejpam-587 102 7 3 3 NUM ejpam-587 102 8 ( ( PUNCT ejpam-587 102 9 2010 2010 NUM ejpam-587 102 10 ) ) PUNCT ejpam-587 102 11 , , PUNCT ejpam-587 102 12 730 730 NUM ejpam-587 102 13 - - SYM ejpam-587 102 14 736 736 NUM ejpam-587 102 15 733 733 NUM ejpam-587 102 16 2 2 NUM ejpam-587 102 17 set set VERB ejpam-587 102 18 i i NOUN ejpam-587 102 19 = = SYM ejpam-587 102 20 â â PROPN ejpam-587 102 21 , , PUNCT ejpam-587 102 22 j j PROPN ejpam-587 102 23 = = SYM ejpam-587 102 24 b b PROPN ejpam-587 102 25 , , PUNCT ejpam-587 102 26 k k PROPN ejpam-587 102 27 = = SYM ejpam-587 102 28 c c NOUN ejpam-587 102 29 , , PUNCT ejpam-587 102 30 l l NOUN ejpam-587 103 1 = = PUNCT ejpam-587 103 2 d d PROPN ejpam-587 103 3 , , PUNCT ejpam-587 103 4 the the DET ejpam-587 103 5 equation equation NOUN ejpam-587 103 6 ( ( PUNCT ejpam-587 103 7 2 2 X ejpam-587 103 8 ) ) PUNCT ejpam-587 103 9 becomes become VERB ejpam-587 103 10 : : PUNCT ejpam-587 103 11 bâbcd bâbcd PUNCT ejpam-587 103 12 = = PUNCT ejpam-587 103 13 râbcd râbcd X ejpam-587 103 14 + + CCONJ ejpam-587 103 15 lâd lâd PROPN ejpam-587 103 16 gbc gbc PROPN ejpam-587 103 17 − − PROPN ejpam-587 103 18 lâc lâc PROPN ejpam-587 103 19 gbd gbd PROPN ejpam-587 103 20 + + CCONJ ejpam-587 103 21 lbc lbc PROPN ejpam-587 103 22 gâd gâd PROPN ejpam-587 103 23 − − PROPN ejpam-587 103 24 lbd lbd PROPN ejpam-587 103 25 gâc gâc PROPN ejpam-587 103 26 − − PROPN ejpam-587 103 27 câdωbc+cbacωbd−cbcωbad câdωbc+cbacωbd−cbcωbad NOUN ejpam-587 104 1 + + CCONJ ejpam-587 104 2 cbdωbac+2cabωcd cbdωbac+2cabωcd NUM ejpam-587 104 3 + + CCONJ ejpam-587 104 4 2ccdωâb 2ccdωâb NUM ejpam-587 104 5 using use VERB ejpam-587 104 6 ( ( PUNCT ejpam-587 104 7 1 1 NUM ejpam-587 104 8 ) ) PUNCT ejpam-587 104 9 , , PUNCT ejpam-587 104 10 ( ( PUNCT ejpam-587 104 11 3 3 X ejpam-587 104 12 ) ) PUNCT ejpam-587 104 13 and and CCONJ ejpam-587 104 14 ( ( PUNCT ejpam-587 104 15 4 4 NUM ejpam-587 104 16 ) ) PUNCT ejpam-587 104 17 , , PUNCT ejpam-587 104 18 we we PRON ejpam-587 104 19 obtained obtain VERB ejpam-587 104 20 : : PUNCT ejpam-587 104 21 bâ bâ VERB ejpam-587 104 22 bcd bcd NOUN ejpam-587 104 23 = = PUNCT ejpam-587 104 24 râbcd râbcd VERB ejpam-587 104 25 + + CCONJ ejpam-587 104 26 1 1 NUM ejpam-587 104 27 n+ n+ NUM ejpam-587 104 28 2 2 NUM ejpam-587 104 29 ( ( PUNCT ejpam-587 104 30 rbdδ rbdδ VERB ejpam-587 104 31 a a DET ejpam-587 104 32 c c NOUN ejpam-587 104 33 − − NOUN ejpam-587 104 34 rbcδ rbcδ NOUN ejpam-587 105 1 a a DET ejpam-587 105 2 d d NOUN ejpam-587 105 3 + + CCONJ ejpam-587 105 4 rcdδ rcdδ VERB ejpam-587 105 5 a a DET ejpam-587 105 6 b b NOUN ejpam-587 105 7 ) ) PUNCT ejpam-587 105 8 in in ADP ejpam-587 105 9 the the DET ejpam-587 105 10 same same ADJ ejpam-587 105 11 manner manner NOUN ejpam-587 105 12 we we PRON ejpam-587 105 13 can can AUX ejpam-587 105 14 get get VERB ejpam-587 105 15 the the DET ejpam-587 105 16 other other ADJ ejpam-587 105 17 components component NOUN ejpam-587 105 18 . . PUNCT ejpam-587 106 1 3 3 X ejpam-587 106 2 . . X ejpam-587 106 3 main main ADJ ejpam-587 106 4 results result NOUN ejpam-587 106 5 a. a. NOUN ejpam-587 106 6 gray gray NOUN ejpam-587 107 1 [ [ X ejpam-587 107 2 4 4 X ejpam-587 107 3 ] ] PUNCT ejpam-587 107 4 defined define VERB ejpam-587 107 5 three three NUM ejpam-587 107 6 special special ADJ ejpam-587 107 7 classes class NOUN ejpam-587 107 8 of of ADP ejpam-587 107 9 ah ah INTJ ejpam-587 107 10 - - PUNCT ejpam-587 107 11 manifold manifold NOUN ejpam-587 107 12 , , PUNCT ejpam-587 107 13 which which PRON ejpam-587 107 14 are be AUX ejpam-587 107 15 given give VERB ejpam-587 107 16 as as ADP ejpam-587 107 17 the the DET ejpam-587 107 18 following follow VERB ejpam-587 107 19 form form NOUN ejpam-587 107 20 : : PUNCT ejpam-587 107 21 1 1 X ejpam-587 107 22 . . X ejpam-587 107 23 class class NOUN ejpam-587 107 24 r1 r1 PROPN ejpam-587 107 25 if if SCONJ ejpam-587 107 26 < < X ejpam-587 107 27 r r X ejpam-587 107 28 ( ( PUNCT ejpam-587 107 29 x x INTJ ejpam-587 107 30 , , PUNCT ejpam-587 107 31 y y PROPN ejpam-587 107 32 ) ) PUNCT ejpam-587 107 33 z z NOUN ejpam-587 107 34 , , PUNCT ejpam-587 107 35 w w X ejpam-587 107 36 > > X ejpam-587 107 37 = = SYM ejpam-587 107 38 < < X ejpam-587 107 39 r r X ejpam-587 107 40 ( ( PUNCT ejpam-587 107 41 jx jx PROPN ejpam-587 107 42 , , PUNCT ejpam-587 107 43 jy jy PROPN ejpam-587 107 44 ) ) PUNCT ejpam-587 107 45 z z PROPN ejpam-587 107 46 , , PUNCT ejpam-587 107 47 w w ADP ejpam-587 107 48 > > X ejpam-587 107 49 . . PUNCT ejpam-587 108 1 2 2 X ejpam-587 108 2 . . X ejpam-587 108 3 class class NOUN ejpam-587 108 4 r2 r2 PROPN ejpam-587 108 5 if if SCONJ ejpam-587 108 6 < < X ejpam-587 108 7 r r X ejpam-587 108 8 ( ( PUNCT ejpam-587 108 9 x x INTJ ejpam-587 108 10 , , PUNCT ejpam-587 108 11 y y PROPN ejpam-587 108 12 ) ) PUNCT ejpam-587 108 13 z z NOUN ejpam-587 108 14 , , PUNCT ejpam-587 108 15 w w X ejpam-587 108 16 > > X ejpam-587 108 17 = = SYM ejpam-587 108 18 < < X ejpam-587 108 19 r r X ejpam-587 108 20 ( ( PUNCT ejpam-587 108 21 jx jx PROPN ejpam-587 108 22 , , PUNCT ejpam-587 108 23 jy jy PROPN ejpam-587 108 24 ) ) PUNCT ejpam-587 108 25 z z PROPN ejpam-587 108 26 , , PUNCT ejpam-587 108 27 w w ADP ejpam-587 108 28 > > X ejpam-587 109 1 + + PUNCT ejpam-587 109 2 < < X ejpam-587 109 3 r r NOUN ejpam-587 109 4 ( ( PUNCT ejpam-587 109 5 jx jx PROPN ejpam-587 109 6 , , PUNCT ejpam-587 109 7 y y PROPN ejpam-587 109 8 ) ) PUNCT ejpam-587 109 9 j j PROPN ejpam-587 109 10 z z PROPN ejpam-587 109 11 , , PUNCT ejpam-587 109 12 w w ADP ejpam-587 109 13 > > X ejpam-587 110 1 + + NOUN ejpam-587 110 2 r r NOUN ejpam-587 110 3 < < X ejpam-587 110 4 jx jx PROPN ejpam-587 110 5 , , PUNCT ejpam-587 110 6 y y PROPN ejpam-587 110 7 ) ) PUNCT ejpam-587 110 8 z z PROPN ejpam-587 110 9 , , PUNCT ejpam-587 110 10 jw jw PROPN ejpam-587 110 11 > > X ejpam-587 110 12 . . PROPN ejpam-587 111 1 3 3 X ejpam-587 111 2 . . X ejpam-587 111 3 class class NOUN ejpam-587 111 4 r3 r3 PROPN ejpam-587 111 5 if if SCONJ ejpam-587 111 6 < < X ejpam-587 111 7 r r X ejpam-587 111 8 ( ( PUNCT ejpam-587 111 9 x x INTJ ejpam-587 111 10 , , PUNCT ejpam-587 111 11 y y PROPN ejpam-587 111 12 ) ) PUNCT ejpam-587 111 13 z z NOUN ejpam-587 111 14 , , PUNCT ejpam-587 111 15 w w X ejpam-587 111 16 > > X ejpam-587 111 17 = = SYM ejpam-587 111 18 < < X ejpam-587 111 19 r r X ejpam-587 111 20 ( ( PUNCT ejpam-587 111 21 jx jx PROPN ejpam-587 111 22 , , PUNCT ejpam-587 111 23 jy jy PROPN ejpam-587 111 24 ) ) PUNCT ejpam-587 112 1 j j PROPN ejpam-587 112 2 z z PROPN ejpam-587 112 3 , , PUNCT ejpam-587 112 4 jw jw PROPN ejpam-587 112 5 > > X ejpam-587 112 6 . . PUNCT ejpam-587 113 1 gray gray PROPN ejpam-587 113 2 proved prove VERB ejpam-587 113 3 that that SCONJ ejpam-587 113 4 for for ADP ejpam-587 113 5 a a DET ejpam-587 113 6 random random ADJ ejpam-587 113 7 ah ah INTJ ejpam-587 113 8 - - PUNCT ejpam-587 113 9 manifold manifold ADJ ejpam-587 113 10 , , PUNCT ejpam-587 113 11 the the DET ejpam-587 113 12 relation relation NOUN ejpam-587 113 13 among among ADP ejpam-587 113 14 them they PRON ejpam-587 113 15 is be AUX ejpam-587 113 16 , , PUNCT ejpam-587 113 17 r1 r1 PROPN ejpam-587 113 18 ⊂ ⊂ PROPN ejpam-587 113 19 r2 r2 PROPN ejpam-587 113 20 ⊂ ⊂ PROPN ejpam-587 113 21 r3 r3 PROPN ejpam-587 113 22 . . PUNCT ejpam-587 114 1 the the DET ejpam-587 114 2 manifold manifold NOUN ejpam-587 114 3 of of ADP ejpam-587 114 4 class class NOUN ejpam-587 114 5 r1 r1 PROPN ejpam-587 114 6 is be AUX ejpam-587 114 7 called call VERB ejpam-587 114 8 a a DET ejpam-587 114 9 parakahler parakahler NOUN ejpam-587 114 10 manifold manifold NOUN ejpam-587 114 11 [ [ X ejpam-587 114 12 12 12 NUM ejpam-587 114 13 ] ] PUNCT ejpam-587 114 14 . . PUNCT ejpam-587 115 1 the the DET ejpam-587 115 2 manifold manifold NOUN ejpam-587 115 3 of of ADP ejpam-587 115 4 class class NOUN ejpam-587 115 5 r3 r3 PROPN ejpam-587 115 6 has have AUX ejpam-587 115 7 been be AUX ejpam-587 115 8 studied study VERB ejpam-587 115 9 by by ADP ejpam-587 115 10 the the DET ejpam-587 115 11 name name NOUN ejpam-587 115 12 rk rk NOUN ejpam-587 115 13 - - PUNCT ejpam-587 115 14 manifold manifold ADJ ejpam-587 115 15 [ [ X ejpam-587 115 16 17 17 NUM ejpam-587 115 17 ] ] PUNCT ejpam-587 115 18 . . PUNCT ejpam-587 116 1 the the DET ejpam-587 116 2 following follow VERB ejpam-587 116 3 lemma lemma PROPN ejpam-587 116 4 gives give VERB ejpam-587 116 5 the the DET ejpam-587 116 6 necessary necessary ADJ ejpam-587 116 7 and and CCONJ ejpam-587 116 8 sufficient sufficient ADJ ejpam-587 116 9 conditions condition NOUN ejpam-587 116 10 that that SCONJ ejpam-587 116 11 a a DET ejpam-587 116 12 random random ADJ ejpam-587 116 13 ah ah INTJ ejpam-587 116 14 - - PUNCT ejpam-587 116 15 manifold manifold NOUN ejpam-587 116 16 is be AUX ejpam-587 116 17 one one NUM ejpam-587 116 18 of of ADP ejpam-587 116 19 the the DET ejpam-587 116 20 above above ADJ ejpam-587 116 21 classes class NOUN ejpam-587 116 22 in in ADP ejpam-587 116 23 the the DET ejpam-587 116 24 adjoint adjoint NOUN ejpam-587 116 25 g g NOUN ejpam-587 116 26 - - PUNCT ejpam-587 116 27 space space NOUN ejpam-587 116 28 . . PUNCT ejpam-587 117 1 lemma lemma PROPN ejpam-587 117 2 1 1 NUM ejpam-587 117 3 ( ( PUNCT ejpam-587 117 4 [ [ X ejpam-587 117 5 16 16 NUM ejpam-587 117 6 ] ] PUNCT ejpam-587 117 7 ) ) PUNCT ejpam-587 117 8 . . PUNCT ejpam-587 118 1 in in ADP ejpam-587 118 2 the the DET ejpam-587 118 3 adjoint adjoint NOUN ejpam-587 118 4 g g NOUN ejpam-587 118 5 - - PUNCT ejpam-587 118 6 structure structure NOUN ejpam-587 118 7 space space NOUN ejpam-587 118 8 , , PUNCT ejpam-587 118 9 an an DET ejpam-587 118 10 ah ah INTJ ejpam-587 118 11 - - PUNCT ejpam-587 118 12 manifold manifold NOUN ejpam-587 118 13 is be AUX ejpam-587 118 14 a a DET ejpam-587 118 15 manifold manifold NOUN ejpam-587 118 16 of of ADP ejpam-587 118 17 : : PUNCT ejpam-587 118 18 1 1 X ejpam-587 118 19 . . X ejpam-587 118 20 class class NOUN ejpam-587 118 21 r1 r1 PROPN ejpam-587 118 22 if if SCONJ ejpam-587 118 23 , , PUNCT ejpam-587 118 24 and and CCONJ ejpam-587 118 25 only only ADV ejpam-587 118 26 if if SCONJ ejpam-587 118 27 , , PUNCT ejpam-587 118 28 râbcd râbcd VERB ejpam-587 118 29 = = SYM ejpam-587 118 30 0 0 NUM ejpam-587 118 31 , , PUNCT ejpam-587 118 32 rabcd rabcd ADJ ejpam-587 118 33 = = SYM ejpam-587 118 34 0 0 NUM ejpam-587 118 35 , , PUNCT ejpam-587 118 36 râ râ PROPN ejpam-587 118 37 b̂cd b̂cd NOUN ejpam-587 118 38 = = SYM ejpam-587 118 39 0 0 NUM ejpam-587 118 40 2 2 NUM ejpam-587 118 41 . . PUNCT ejpam-587 118 42 class class NOUN ejpam-587 118 43 r2 r2 PROPN ejpam-587 118 44 if if SCONJ ejpam-587 118 45 , , PUNCT ejpam-587 118 46 and and CCONJ ejpam-587 118 47 only only ADV ejpam-587 118 48 if if SCONJ ejpam-587 118 49 , , PUNCT ejpam-587 118 50 râbcd râbcd VERB ejpam-587 118 51 = = SYM ejpam-587 118 52 0 0 NUM ejpam-587 118 53 , , PUNCT ejpam-587 118 54 rabcd rabcd ADJ ejpam-587 118 55 = = SYM ejpam-587 118 56 0 0 NUM ejpam-587 118 57 3 3 X ejpam-587 118 58 . . PUNCT ejpam-587 118 59 class class NOUN ejpam-587 118 60 r3 r3 PROPN ejpam-587 118 61 if if SCONJ ejpam-587 118 62 , , PUNCT ejpam-587 118 63 and and CCONJ ejpam-587 118 64 only only ADV ejpam-587 118 65 if if SCONJ ejpam-587 118 66 , , PUNCT ejpam-587 118 67 râbcd râbcd VERB ejpam-587 118 68 = = SYM ejpam-587 118 69 0 0 NUM ejpam-587 118 70 recall recall VERB ejpam-587 118 71 that that SCONJ ejpam-587 118 72 an an DET ejpam-587 118 73 ah ah INTJ ejpam-587 118 74 - - PUNCT ejpam-587 118 75 manifold manifold NOUN ejpam-587 118 76 has have VERB ejpam-587 118 77 j j PROPN ejpam-587 118 78 - - PUNCT ejpam-587 118 79 invariant invariant ADJ ejpam-587 118 80 ricci ricci PROPN ejpam-587 118 81 tensor tensor NOUN ejpam-587 118 82 if if SCONJ ejpam-587 118 83 , , PUNCT ejpam-587 118 84 r r NOUN ejpam-587 118 85 ◦ ◦ NOUN ejpam-587 118 86 j= j= NOUN ejpam-587 118 87 j j PROPN ejpam-587 119 1 ◦ ◦ NOUN ejpam-587 119 2 r r NOUN ejpam-587 120 1 [ [ X ejpam-587 120 2 16 16 NUM ejpam-587 120 3 ] ] PUNCT ejpam-587 120 4 . . PUNCT ejpam-587 121 1 lemma lemma PROPN ejpam-587 121 2 2 2 NUM ejpam-587 121 3 ( ( PUNCT ejpam-587 121 4 [ [ X ejpam-587 121 5 16 16 NUM ejpam-587 121 6 ] ] NUM ejpam-587 121 7 ) ) PUNCT ejpam-587 121 8 . . PUNCT ejpam-587 122 1 an an DET ejpam-587 122 2 ah ah INTJ ejpam-587 122 3 - - PUNCT ejpam-587 122 4 manifold manifold NOUN ejpam-587 122 5 has have AUX ejpam-587 122 6 j j PROPN ejpam-587 122 7 - - PUNCT ejpam-587 122 8 invariant invariant ADJ ejpam-587 122 9 ricci ricci PROPN ejpam-587 122 10 tensor tensor NOUN ejpam-587 122 11 if if SCONJ ejpam-587 122 12 , , PUNCT ejpam-587 122 13 and and CCONJ ejpam-587 122 14 only only ADV ejpam-587 122 15 if if SCONJ ejpam-587 122 16 , , PUNCT ejpam-587 122 17 in in ADP ejpam-587 122 18 the the DET ejpam-587 122 19 adjoint adjoint NOUN ejpam-587 122 20 g g NOUN ejpam-587 122 21 - - PUNCT ejpam-587 122 22 structure structure NOUN ejpam-587 122 23 space space NOUN ejpam-587 122 24 , , PUNCT ejpam-587 122 25 rab rab PROPN ejpam-587 122 26 = = SYM ejpam-587 122 27 0 0 PROPN ejpam-587 122 28 . . PUNCT ejpam-587 122 29 theorem theorem NOUN ejpam-587 122 30 1 1 NUM ejpam-587 122 31 . . PUNCT ejpam-587 122 32 suppose suppose VERB ejpam-587 122 33 that that SCONJ ejpam-587 122 34 m m PROPN ejpam-587 122 35 is be AUX ejpam-587 122 36 ah ah INTJ ejpam-587 122 37 - - PUNCT ejpam-587 122 38 manifold manifold ADJ ejpam-587 122 39 with with ADP ejpam-587 122 40 flat flat ADJ ejpam-587 122 41 bochner bochner NOUN ejpam-587 122 42 tensor tensor NOUN ejpam-587 122 43 , , PUNCT ejpam-587 122 44 then then ADV ejpam-587 122 45 m m VERB ejpam-587 122 46 is be AUX ejpam-587 122 47 a a DET ejpam-587 122 48 manifold manifold NOUN ejpam-587 122 49 of of ADP ejpam-587 122 50 class class NOUN ejpam-587 122 51 r3 r3 PROPN ejpam-587 122 52 if if SCONJ ejpam-587 122 53 , , PUNCT ejpam-587 122 54 and and CCONJ ejpam-587 122 55 only only ADV ejpam-587 122 56 if if SCONJ ejpam-587 122 57 , , PUNCT ejpam-587 122 58 m m VERB ejpam-587 122 59 is be AUX ejpam-587 122 60 linear linear ADJ ejpam-587 122 61 complex complex ADJ ejpam-587 122 62 manifold manifold NOUN ejpam-587 122 63 . . PUNCT ejpam-587 123 1 h. h. PROPN ejpam-587 123 2 abood abood PROPN ejpam-587 123 3 / / SYM ejpam-587 123 4 eur eur PROPN ejpam-587 123 5 . . PUNCT ejpam-587 124 1 j. j. PROPN ejpam-587 124 2 pure pure PROPN ejpam-587 124 3 appl appl PROPN ejpam-587 124 4 . . PROPN ejpam-587 124 5 math math PROPN ejpam-587 124 6 , , PUNCT ejpam-587 124 7 3 3 NUM ejpam-587 124 8 ( ( PUNCT ejpam-587 124 9 2010 2010 NUM ejpam-587 124 10 ) ) PUNCT ejpam-587 124 11 , , PUNCT ejpam-587 124 12 730 730 NUM ejpam-587 124 13 - - SYM ejpam-587 124 14 736 736 NUM ejpam-587 124 15 734 734 NUM ejpam-587 124 16 proof proof NOUN ejpam-587 124 17 . . PUNCT ejpam-587 125 1 by by ADP ejpam-587 125 2 proposition proposition NOUN ejpam-587 125 3 1 1 NUM ejpam-587 125 4 we we PRON ejpam-587 125 5 have have AUX ejpam-587 125 6 : : PUNCT ejpam-587 125 7 bâ bâ VERB ejpam-587 125 8 bcd bcd NOUN ejpam-587 125 9 = = PUNCT ejpam-587 125 10 râbcd râbcd VERB ejpam-587 125 11 + + CCONJ ejpam-587 125 12 1 1 NUM ejpam-587 125 13 n+ n+ NUM ejpam-587 125 14 2 2 NUM ejpam-587 125 15 ( ( PUNCT ejpam-587 125 16 rbdδ rbdδ VERB ejpam-587 125 17 a a DET ejpam-587 125 18 c c NOUN ejpam-587 125 19 − − NOUN ejpam-587 125 20 rbcδ rbcδ NOUN ejpam-587 126 1 a a DET ejpam-587 126 2 d d NOUN ejpam-587 126 3 + + CCONJ ejpam-587 126 4 rcdδ rcdδ VERB ejpam-587 126 5 a a DET ejpam-587 126 6 b b NOUN ejpam-587 126 7 ) ) PUNCT ejpam-587 126 8 suppose suppose VERB ejpam-587 126 9 that that SCONJ ejpam-587 126 10 m m PROPN ejpam-587 126 11 is be AUX ejpam-587 126 12 ah ah INTJ ejpam-587 126 13 - - PUNCT ejpam-587 126 14 manifold manifold NOUN ejpam-587 126 15 of of ADP ejpam-587 126 16 class class NOUN ejpam-587 126 17 r3 r3 PROPN ejpam-587 126 18 with with ADP ejpam-587 126 19 flat flat ADJ ejpam-587 126 20 bochner bochner NOUN ejpam-587 126 21 tensor tensor NOUN ejpam-587 126 22 . . PUNCT ejpam-587 127 1 that that PRON ejpam-587 127 2 means mean VERB ejpam-587 127 3 bâbcd bâbcd PUNCT ejpam-587 127 4 = = SYM ejpam-587 127 5 0 0 NUM ejpam-587 127 6 and and CCONJ ejpam-587 127 7 râbcd râbcd NUM ejpam-587 127 8 = = SYM ejpam-587 127 9 0 0 X ejpam-587 127 10 . . PUNCT ejpam-587 128 1 thus thus ADV ejpam-587 128 2 we we PRON ejpam-587 128 3 get get AUX ejpam-587 128 4 : : PUNCT ejpam-587 128 5 rbdδ rbdδ VERB ejpam-587 128 6 a a DET ejpam-587 128 7 c c NOUN ejpam-587 128 8 − − NOUN ejpam-587 128 9 rbcδ rbcδ NOUN ejpam-587 129 1 a a DET ejpam-587 129 2 d d NOUN ejpam-587 130 1 + + CCONJ ejpam-587 130 2 rcdδ rcdδ VERB ejpam-587 130 3 a a DET ejpam-587 130 4 b b NOUN ejpam-587 130 5 = = SYM ejpam-587 130 6 0 0 NUM ejpam-587 130 7 ( ( PUNCT ejpam-587 130 8 5 5 NUM ejpam-587 130 9 ) ) PUNCT ejpam-587 130 10 contracting contracting NOUN ejpam-587 130 11 ( ( PUNCT ejpam-587 130 12 5 5 NUM ejpam-587 130 13 ) ) PUNCT ejpam-587 130 14 by by ADP ejpam-587 130 15 the the DET ejpam-587 130 16 indexes index NOUN ejpam-587 130 17 c c NOUN ejpam-587 130 18 and and CCONJ ejpam-587 130 19 a a PRON ejpam-587 130 20 , , PUNCT ejpam-587 130 21 we we PRON ejpam-587 130 22 obtained obtain VERB ejpam-587 130 23 : : PUNCT ejpam-587 130 24 nrbd nrbd VERB ejpam-587 130 25 − − PROPN ejpam-587 130 26 rbd rbd NOUN ejpam-587 130 27 + + CCONJ ejpam-587 130 28 rbd rbd NOUN ejpam-587 130 29 = = SYM ejpam-587 130 30 0 0 NUM ejpam-587 130 31 which which PRON ejpam-587 130 32 means mean VERB ejpam-587 130 33 that that SCONJ ejpam-587 130 34 rbd rbd NOUN ejpam-587 130 35 = = PUNCT ejpam-587 130 36 0 0 PROPN ejpam-587 130 37 . . PUNCT ejpam-587 131 1 by by ADP ejpam-587 131 2 lemma lemma PROPN ejpam-587 131 3 2 2 NUM ejpam-587 131 4 we we PRON ejpam-587 131 5 have have VERB ejpam-587 131 6 rbd rbd NOUN ejpam-587 131 7 = = SYM ejpam-587 131 8 0 0 PUNCT ejpam-587 132 1 if if SCONJ ejpam-587 132 2 , , PUNCT ejpam-587 132 3 and and CCONJ ejpam-587 132 4 only only ADV ejpam-587 132 5 if if SCONJ ejpam-587 132 6 , , PUNCT ejpam-587 132 7 r r NOUN ejpam-587 132 8 ◦ ◦ NOUN ejpam-587 132 9 j j PROPN ejpam-587 132 10 = = SYM ejpam-587 132 11 j j PROPN ejpam-587 132 12 ◦ ◦ PROPN ejpam-587 132 13 r. r. PROPN ejpam-587 132 14 hence hence ADV ejpam-587 132 15 , , PUNCT ejpam-587 132 16 from from ADP ejpam-587 132 17 [ [ X ejpam-587 132 18 2 2 X ejpam-587 132 19 ] ] PUNCT ejpam-587 132 20 m m VERB ejpam-587 132 21 is be AUX ejpam-587 132 22 linear linear ADJ ejpam-587 132 23 complex complex ADJ ejpam-587 132 24 manifold manifold NOUN ejpam-587 132 25 . . PUNCT ejpam-587 133 1 corollary corollary ADJ ejpam-587 133 2 1 1 PROPN ejpam-587 133 3 . . PUNCT ejpam-587 133 4 suppose suppose VERB ejpam-587 133 5 that that SCONJ ejpam-587 133 6 m m PROPN ejpam-587 133 7 is be AUX ejpam-587 133 8 an an DET ejpam-587 133 9 ah ah INTJ ejpam-587 133 10 - - PUNCT ejpam-587 133 11 manifold manifold NOUN ejpam-587 133 12 with with ADP ejpam-587 133 13 flat flat ADJ ejpam-587 133 14 bochner bochner NOUN ejpam-587 133 15 tensor tensor NOUN ejpam-587 133 16 , , PUNCT ejpam-587 133 17 then then ADV ejpam-587 133 18 m m VERB ejpam-587 133 19 is be AUX ejpam-587 133 20 a a DET ejpam-587 133 21 manifold manifold NOUN ejpam-587 133 22 of of ADP ejpam-587 133 23 class class NOUN ejpam-587 133 24 r3 r3 PROPN ejpam-587 133 25 if if SCONJ ejpam-587 133 26 , , PUNCT ejpam-587 133 27 and and CCONJ ejpam-587 133 28 only only ADV ejpam-587 133 29 if if SCONJ ejpam-587 133 30 , , PUNCT ejpam-587 133 31 m m VERB ejpam-587 133 32 is be AUX ejpam-587 133 33 a a DET ejpam-587 133 34 manifold manifold NOUN ejpam-587 133 35 of of ADP ejpam-587 133 36 class class NOUN ejpam-587 133 37 r2 r2 NOUN ejpam-587 133 38 . . PUNCT ejpam-587 134 1 proof proof NOUN ejpam-587 134 2 . . PUNCT ejpam-587 135 1 this this PRON ejpam-587 135 2 is be AUX ejpam-587 135 3 directly directly ADV ejpam-587 135 4 from from ADP ejpam-587 135 5 the the DET ejpam-587 135 6 condition condition NOUN ejpam-587 135 7 of of ADP ejpam-587 135 8 the the DET ejpam-587 135 9 class class NOUN ejpam-587 135 10 r2 r2 PROPN ejpam-587 135 11 . . PUNCT ejpam-587 136 1 theorem theorem NOUN ejpam-587 136 2 2 2 NUM ejpam-587 136 3 . . PUNCT ejpam-587 136 4 suppose suppose VERB ejpam-587 136 5 that that SCONJ ejpam-587 136 6 m m PROPN ejpam-587 136 7 is be AUX ejpam-587 136 8 an an DET ejpam-587 136 9 ah ah INTJ ejpam-587 136 10 - - PUNCT ejpam-587 136 11 manifold manifold NOUN ejpam-587 136 12 with with ADP ejpam-587 136 13 flat flat ADJ ejpam-587 136 14 bochner bochner NOUN ejpam-587 136 15 tensor tensor NOUN ejpam-587 136 16 . . PUNCT ejpam-587 137 1 if if SCONJ ejpam-587 137 2 m m NOUN ejpam-587 137 3 is be AUX ejpam-587 137 4 a a DET ejpam-587 137 5 manifold manifold NOUN ejpam-587 137 6 of of ADP ejpam-587 137 7 class class NOUN ejpam-587 137 8 r1 r1 PROPN ejpam-587 137 9 , , PUNCT ejpam-587 137 10 then then ADV ejpam-587 137 11 m m NOUN ejpam-587 137 12 is be AUX ejpam-587 137 13 either either CCONJ ejpam-587 137 14 n n CCONJ ejpam-587 137 15 - - PUNCT ejpam-587 137 16 dimensional dimensional ADJ ejpam-587 137 17 ricci ricci PROPN ejpam-587 137 18 flat flat PROPN ejpam-587 137 19 manifold manifold NOUN ejpam-587 137 20 for for ADP ejpam-587 137 21 n n CCONJ ejpam-587 137 22 > > SYM ejpam-587 137 23 2 2 NUM ejpam-587 137 24 or or CCONJ ejpam-587 137 25 2 2 NUM ejpam-587 137 26 - - PUNCT ejpam-587 137 27 dimensional dimensional ADJ ejpam-587 137 28 flat flat ADJ ejpam-587 137 29 scalar scalar ADJ ejpam-587 137 30 curvature curvature NOUN ejpam-587 137 31 manifold manifold ADJ ejpam-587 137 32 . . PUNCT ejpam-587 138 1 proof proof NOUN ejpam-587 138 2 . . PUNCT ejpam-587 139 1 suppose suppose VERB ejpam-587 139 2 that that SCONJ ejpam-587 139 3 m m PROPN ejpam-587 139 4 is be AUX ejpam-587 139 5 ah ah INTJ ejpam-587 139 6 - - PUNCT ejpam-587 139 7 manifold manifold NOUN ejpam-587 139 8 of of ADP ejpam-587 139 9 class class NOUN ejpam-587 139 10 r1 r1 NOUN ejpam-587 139 11 with with ADP ejpam-587 139 12 flat flat ADJ ejpam-587 139 13 bochner bochner NOUN ejpam-587 139 14 tensor tensor NOUN ejpam-587 139 15 . . PUNCT ejpam-587 140 1 according accord VERB ejpam-587 140 2 to to ADP ejpam-587 140 3 lemma lemma PROPN ejpam-587 140 4 1 1 NUM ejpam-587 140 5 we we PRON ejpam-587 140 6 have have AUX ejpam-587 140 7 râbcd râbcd VERB ejpam-587 140 8 = = SYM ejpam-587 140 9 0 0 NUM ejpam-587 140 10 , , PUNCT ejpam-587 140 11 rabcd rabcd VERB ejpam-587 140 12 = = SYM ejpam-587 140 13 0 0 NUM ejpam-587 140 14 , , PUNCT ejpam-587 140 15 râ râ PROPN ejpam-587 140 16 b̂cd b̂cd NOUN ejpam-587 140 17 = = SYM ejpam-587 140 18 0 0 X ejpam-587 140 19 . . PUNCT ejpam-587 141 1 thus thus ADV ejpam-587 141 2 ra ra PROPN ejpam-587 142 1 c c PROPN ejpam-587 142 2 δ δ PROPN ejpam-587 142 3 b b PROPN ejpam-587 143 1 d d NOUN ejpam-587 143 2 − − PROPN ejpam-587 143 3 ra ra PROPN ejpam-587 144 1 d d PROPN ejpam-587 144 2 δ δ PROPN ejpam-587 144 3 b b PROPN ejpam-587 145 1 c c PROPN ejpam-587 146 1 + + NOUN ejpam-587 146 2 r r NOUN ejpam-587 146 3 b b PROPN ejpam-587 146 4 d d PROPN ejpam-587 146 5 δ δ PROPN ejpam-587 146 6 a a DET ejpam-587 146 7 c c NOUN ejpam-587 147 1 − − NOUN ejpam-587 147 2 r r NOUN ejpam-587 147 3 b b PROPN ejpam-587 147 4 c c NOUN ejpam-587 147 5 δ δ PROPN ejpam-587 147 6 a a X ejpam-587 147 7 d d X ejpam-587 147 8 = = SYM ejpam-587 147 9 0 0 NUM ejpam-587 147 10 ( ( PUNCT ejpam-587 147 11 6 6 NUM ejpam-587 147 12 ) ) PUNCT ejpam-587 147 13 contracting contract VERB ejpam-587 147 14 the the DET ejpam-587 147 15 equation equation NOUN ejpam-587 147 16 ( ( PUNCT ejpam-587 147 17 6 6 NUM ejpam-587 147 18 ) ) PUNCT ejpam-587 147 19 by by ADP ejpam-587 147 20 the the DET ejpam-587 147 21 indexes index NOUN ejpam-587 147 22 a a PRON ejpam-587 147 23 and and CCONJ ejpam-587 147 24 c c AUX ejpam-587 147 25 we we PRON ejpam-587 147 26 get get VERB ejpam-587 147 27 : : PUNCT ejpam-587 148 1 ra ra PROPN ejpam-587 149 1 aδ aδ PROPN ejpam-587 149 2 b b PROPN ejpam-587 150 1 d d NOUN ejpam-587 150 2 − − PROPN ejpam-587 150 3 r r NOUN ejpam-587 150 4 b b PROPN ejpam-587 150 5 d d PROPN ejpam-587 150 6 + + PROPN ejpam-587 150 7 nr nr PROPN ejpam-587 150 8 b b PROPN ejpam-587 150 9 d d NOUN ejpam-587 150 10 − − PROPN ejpam-587 150 11 r r NOUN ejpam-587 150 12 b b PROPN ejpam-587 150 13 d d NOUN ejpam-587 150 14 = = SYM ejpam-587 150 15 0 0 NUM ejpam-587 150 16 ( ( PUNCT ejpam-587 150 17 7 7 X ejpam-587 150 18 ) ) PUNCT ejpam-587 150 19 contracting contract VERB ejpam-587 150 20 the the DET ejpam-587 150 21 equation equation NOUN ejpam-587 150 22 ( ( PUNCT ejpam-587 150 23 7 7 NUM ejpam-587 150 24 ) ) PUNCT ejpam-587 150 25 by by ADP ejpam-587 150 26 the the DET ejpam-587 150 27 indexes index NOUN ejpam-587 150 28 b b NOUN ejpam-587 150 29 and and CCONJ ejpam-587 150 30 d d NOUN ejpam-587 150 31 we we PRON ejpam-587 150 32 obtained obtain VERB ejpam-587 150 33 : : PUNCT ejpam-587 150 34 nra nra PROPN ejpam-587 150 35 a a DET ejpam-587 150 36 − − PROPN ejpam-587 150 37 ra ra PROPN ejpam-587 151 1 a a DET ejpam-587 151 2 + + X ejpam-587 151 3 nra nra NOUN ejpam-587 151 4 a a DET ejpam-587 151 5 − − PROPN ejpam-587 151 6 ra ra PROPN ejpam-587 151 7 a a DET ejpam-587 151 8 = = NOUN ejpam-587 151 9 0 0 PUNCT ejpam-587 152 1 hence hence ADV ejpam-587 152 2 ra ra PROPN ejpam-587 152 3 a a DET ejpam-587 152 4 = = NOUN ejpam-587 152 5 0 0 NUM ejpam-587 152 6 thus thus ADV ejpam-587 152 7 , , PUNCT ejpam-587 152 8 the the DET ejpam-587 152 9 equation equation NOUN ejpam-587 152 10 ( ( PUNCT ejpam-587 152 11 7 7 X ejpam-587 152 12 ) ) PUNCT ejpam-587 152 13 will will AUX ejpam-587 152 14 be be AUX ejpam-587 152 15 as as ADP ejpam-587 152 16 the the DET ejpam-587 152 17 form form NOUN ejpam-587 152 18 : : PUNCT ejpam-587 152 19 ( ( PUNCT ejpam-587 152 20 n− n− NOUN ejpam-587 152 21 2 2 NUM ejpam-587 152 22 ) ) PUNCT ejpam-587 152 23 r r NOUN ejpam-587 152 24 b b NOUN ejpam-587 152 25 d d NOUN ejpam-587 152 26 = = SYM ejpam-587 152 27 0 0 PUNCT ejpam-587 152 28 if if SCONJ ejpam-587 152 29 n n PROPN ejpam-587 152 30 6= 6= NUM ejpam-587 152 31 2 2 NUM ejpam-587 152 32 we we PRON ejpam-587 152 33 get get VERB ejpam-587 152 34 : : PUNCT ejpam-587 152 35 r r NOUN ejpam-587 152 36 b b PROPN ejpam-587 152 37 d d NOUN ejpam-587 152 38 = = SYM ejpam-587 152 39 0 0 NUM ejpam-587 153 1 therefore therefore ADV ejpam-587 153 2 m m PROPN ejpam-587 153 3 is be AUX ejpam-587 153 4 ricci ricci PROPN ejpam-587 153 5 flat flat ADJ ejpam-587 153 6 manifold manifold NOUN ejpam-587 153 7 . . PUNCT ejpam-587 154 1 if if SCONJ ejpam-587 154 2 n= n= ADJ ejpam-587 154 3 2 2 NUM ejpam-587 154 4 , , PUNCT ejpam-587 154 5 we we PRON ejpam-587 154 6 shall shall AUX ejpam-587 154 7 discuss discuss VERB ejpam-587 154 8 the the DET ejpam-587 154 9 cases case NOUN ejpam-587 154 10 of of ADP ejpam-587 154 11 the the DET ejpam-587 154 12 values value NOUN ejpam-587 154 13 a a DET ejpam-587 154 14 , , PUNCT ejpam-587 154 15 b b PROPN ejpam-587 154 16 , , PUNCT ejpam-587 154 17 c c NOUN ejpam-587 154 18 , , PUNCT ejpam-587 154 19 and and CCONJ ejpam-587 154 20 d d X ejpam-587 154 21 in in ADP ejpam-587 154 22 the the DET ejpam-587 154 23 equation equation NOUN ejpam-587 154 24 ( ( PUNCT ejpam-587 154 25 6 6 NUM ejpam-587 154 26 ): ): PUNCT ejpam-587 154 27 h. h. PROPN ejpam-587 154 28 abood abood PROPN ejpam-587 154 29 / / SYM ejpam-587 154 30 eur eur PROPN ejpam-587 154 31 . . PUNCT ejpam-587 155 1 j. j. PROPN ejpam-587 155 2 pure pure PROPN ejpam-587 155 3 appl appl PROPN ejpam-587 155 4 . . PROPN ejpam-587 155 5 math math PROPN ejpam-587 155 6 , , PUNCT ejpam-587 155 7 3 3 NUM ejpam-587 155 8 ( ( PUNCT ejpam-587 155 9 2010 2010 NUM ejpam-587 155 10 ) ) PUNCT ejpam-587 155 11 , , PUNCT ejpam-587 155 12 730 730 NUM ejpam-587 155 13 - - SYM ejpam-587 155 14 736 736 NUM ejpam-587 155 15 735 735 NUM ejpam-587 155 16 1 1 NUM ejpam-587 155 17 . . PUNCT ejpam-587 155 18 put put VERB ejpam-587 155 19 a a DET ejpam-587 155 20 = = ADJ ejpam-587 155 21 2 2 NUM ejpam-587 155 22 , , PUNCT ejpam-587 155 23 b b NOUN ejpam-587 155 24 = = SYM ejpam-587 155 25 2 2 NUM ejpam-587 155 26 , , PUNCT ejpam-587 155 27 c c NOUN ejpam-587 155 28 = = SYM ejpam-587 155 29 1 1 NUM ejpam-587 155 30 , , PUNCT ejpam-587 155 31 d d NOUN ejpam-587 155 32 = = SYM ejpam-587 155 33 1 1 NUM ejpam-587 155 34 we we PRON ejpam-587 155 35 get get VERB ejpam-587 155 36 : : PUNCT ejpam-587 155 37 r1 r1 NOUN ejpam-587 155 38 1 1 NUM ejpam-587 155 39 + + NUM ejpam-587 155 40 r2 r2 PROPN ejpam-587 155 41 2 2 NUM ejpam-587 155 42 = = SYM ejpam-587 155 43 0 0 NUM ejpam-587 155 44 2 2 NUM ejpam-587 155 45 . . PUNCT ejpam-587 155 46 put put VERB ejpam-587 155 47 a a DET ejpam-587 155 48 = = ADJ ejpam-587 155 49 2 2 NUM ejpam-587 155 50 , , PUNCT ejpam-587 155 51 b b NOUN ejpam-587 155 52 = = SYM ejpam-587 155 53 1 1 NUM ejpam-587 155 54 , , PUNCT ejpam-587 155 55 c c NOUN ejpam-587 155 56 = = SYM ejpam-587 155 57 1 1 NUM ejpam-587 155 58 , , PUNCT ejpam-587 155 59 d d NOUN ejpam-587 155 60 = = SYM ejpam-587 155 61 2 2 NUM ejpam-587 155 62 we we PRON ejpam-587 155 63 get get VERB ejpam-587 155 64 : : PUNCT ejpam-587 155 65 −r1 −r1 PROPN ejpam-587 155 66 1− 1− NUM ejpam-587 155 67 r2 r2 PROPN ejpam-587 155 68 2 2 NUM ejpam-587 155 69 = = SYM ejpam-587 155 70 0 0 NUM ejpam-587 156 1 thus thus ADV ejpam-587 156 2 in in ADP ejpam-587 156 3 all all DET ejpam-587 156 4 possible possible ADJ ejpam-587 156 5 other other ADJ ejpam-587 156 6 cases case NOUN ejpam-587 156 7 of of ADP ejpam-587 156 8 the the DET ejpam-587 156 9 values value NOUN ejpam-587 156 10 a a DET ejpam-587 156 11 , , PUNCT ejpam-587 156 12 b b PROPN ejpam-587 156 13 , , PUNCT ejpam-587 156 14 c c NOUN ejpam-587 156 15 , , PUNCT ejpam-587 156 16 and and CCONJ ejpam-587 156 17 d d NOUN ejpam-587 156 18 we we PRON ejpam-587 156 19 obtained obtain VERB ejpam-587 156 20 : : PUNCT ejpam-587 156 21 r1 r1 PROPN ejpam-587 156 22 1 1 NUM ejpam-587 156 23 + + NUM ejpam-587 156 24 r2 r2 PROPN ejpam-587 156 25 2 2 NUM ejpam-587 156 26 = = SYM ejpam-587 156 27 0 0 NUM ejpam-587 156 28 or or CCONJ ejpam-587 156 29 −r1 −r1 PROPN ejpam-587 156 30 1 1 NUM ejpam-587 156 31 − − NOUN ejpam-587 156 32 r2 r2 NOUN ejpam-587 156 33 2 2 NUM ejpam-587 156 34 = = SYM ejpam-587 156 35 0 0 NUM ejpam-587 157 1 this this PRON ejpam-587 157 2 means mean VERB ejpam-587 157 3 r r NOUN ejpam-587 157 4 i i PRON ejpam-587 157 5 i i NOUN ejpam-587 157 6 = = NOUN ejpam-587 157 7 0 0 X ejpam-587 157 8 . . PUNCT ejpam-587 158 1 it it PRON ejpam-587 158 2 is be AUX ejpam-587 158 3 well well ADV ejpam-587 158 4 known know VERB ejpam-587 158 5 , , PUNCT ejpam-587 158 6 that that SCONJ ejpam-587 158 7 the the DET ejpam-587 158 8 scalar scalar ADJ ejpam-587 158 9 curvature curvature NOUN ejpam-587 158 10 tensor tensor NOUN ejpam-587 158 11 is be AUX ejpam-587 158 12 given give VERB ejpam-587 158 13 by by ADP ejpam-587 158 14 the the DET ejpam-587 158 15 form form NOUN ejpam-587 158 16 k k NOUN ejpam-587 159 1 = = PUNCT ejpam-587 159 2 r r NOUN ejpam-587 159 3 i i PRON ejpam-587 160 1 i i INTJ ejpam-587 160 2 . . PUNCT ejpam-587 161 1 therefore therefore ADV ejpam-587 161 2 m m PROPN ejpam-587 161 3 is be AUX ejpam-587 161 4 a a DET ejpam-587 161 5 manifold manifold NOUN ejpam-587 161 6 of of ADP ejpam-587 161 7 flat flat ADJ ejpam-587 161 8 scalar scalar ADJ ejpam-587 161 9 curvature curvature NOUN ejpam-587 161 10 tensor tensor NOUN ejpam-587 161 11 . . PUNCT ejpam-587 162 1 theorem theorem NOUN ejpam-587 162 2 3 3 X ejpam-587 162 3 . . PUNCT ejpam-587 162 4 suppose suppose VERB ejpam-587 162 5 that that SCONJ ejpam-587 162 6 m m PROPN ejpam-587 162 7 is be AUX ejpam-587 162 8 ah ah INTJ ejpam-587 162 9 - - PUNCT ejpam-587 162 10 manifold manifold ADJ ejpam-587 162 11 with with ADP ejpam-587 162 12 flat flat ADJ ejpam-587 162 13 bochner bochner NOUN ejpam-587 162 14 tensor tensor NOUN ejpam-587 162 15 , , PUNCT ejpam-587 162 16 if if SCONJ ejpam-587 162 17 m m NOUN ejpam-587 162 18 is be AUX ejpam-587 162 19 flat flat ADJ ejpam-587 162 20 manifold manifold NOUN ejpam-587 162 21 , , PUNCT ejpam-587 162 22 then then ADV ejpam-587 162 23 m m VERB ejpam-587 162 24 is be AUX ejpam-587 162 25 an an DET ejpam-587 162 26 einstein einstein NOUN ejpam-587 162 27 manifold manifold NOUN ejpam-587 162 28 with with ADP ejpam-587 162 29 cosmological cosmological ADJ ejpam-587 162 30 constant constant ADJ ejpam-587 162 31 k k PROPN ejpam-587 162 32 2n 2n NUM ejpam-587 162 33 . . PUNCT ejpam-587 163 1 proof proof NOUN ejpam-587 163 2 . . PUNCT ejpam-587 164 1 by by ADP ejpam-587 164 2 the the DET ejpam-587 164 3 proposition proposition NOUN ejpam-587 164 4 1 1 NUM ejpam-587 164 5 we we PRON ejpam-587 164 6 have have VERB ejpam-587 164 7 : : PUNCT ejpam-587 164 8 bâbcd̂ bâbcd̂ X ejpam-587 164 9 = = PUNCT ejpam-587 164 10 râbcd̂ râbcd̂ NOUN ejpam-587 165 1 + + SYM ejpam-587 165 2 1 1 NUM ejpam-587 165 3 n+ n+ SYM ejpam-587 165 4 2 2 NUM ejpam-587 165 5 ( ( PUNCT ejpam-587 165 6 ra ra NOUN ejpam-587 165 7 bδ bδ PROPN ejpam-587 165 8 d d PROPN ejpam-587 165 9 c c PROPN ejpam-587 165 10 − − PROPN ejpam-587 165 11 rd rd PROPN ejpam-587 165 12 c c PROPN ejpam-587 165 13 δ δ PROPN ejpam-587 165 14 a a DET ejpam-587 165 15 b b NOUN ejpam-587 165 16 ) ) PUNCT ejpam-587 165 17 suppose suppose VERB ejpam-587 165 18 that that SCONJ ejpam-587 165 19 m m PROPN ejpam-587 165 20 is be AUX ejpam-587 165 21 flat flat ADJ ejpam-587 165 22 manifold manifold ADJ ejpam-587 165 23 with with ADP ejpam-587 165 24 flat flat ADJ ejpam-587 165 25 bochner bochner NOUN ejpam-587 165 26 tensor tensor NOUN ejpam-587 165 27 . . PUNCT ejpam-587 166 1 this this PRON ejpam-587 166 2 means mean VERB ejpam-587 166 3 that that SCONJ ejpam-587 166 4 the the DET ejpam-587 166 5 riemannian riemannian ADJ ejpam-587 166 6 and and CCONJ ejpam-587 166 7 bochner bochn ADJ ejpam-587 166 8 tensors tensor NOUN ejpam-587 166 9 are be AUX ejpam-587 166 10 vanishing vanish VERB ejpam-587 166 11 . . PUNCT ejpam-587 167 1 thus thus ADV ejpam-587 167 2 we we PRON ejpam-587 167 3 obtained obtain VERB ejpam-587 167 4 : : PUNCT ejpam-587 167 5 ra ra PROPN ejpam-587 167 6 b b PROPN ejpam-587 167 7 δ δ PROPN ejpam-587 167 8 d d PROPN ejpam-587 167 9 c c PROPN ejpam-587 167 10 − − PROPN ejpam-587 167 11 rd rd PROPN ejpam-587 167 12 c c PROPN ejpam-587 167 13 δ δ PROPN ejpam-587 167 14 a a DET ejpam-587 167 15 b b X ejpam-587 167 16 = = SYM ejpam-587 167 17 0 0 NUM ejpam-587 167 18 ( ( PUNCT ejpam-587 167 19 8) 8) NUM ejpam-587 167 20 contracting contracting NOUN ejpam-587 167 21 ( ( PUNCT ejpam-587 167 22 8) 8) NUM ejpam-587 167 23 by by ADP ejpam-587 167 24 the the DET ejpam-587 167 25 indexes index NOUN ejpam-587 167 26 c c NOUN ejpam-587 168 1 and and CCONJ ejpam-587 168 2 d d NOUN ejpam-587 168 3 , , PUNCT ejpam-587 168 4 we we PRON ejpam-587 168 5 get get VERB ejpam-587 168 6 : : PUNCT ejpam-587 169 1 nra nra PROPN ejpam-587 169 2 b b PROPN ejpam-587 169 3 = = SYM ejpam-587 170 1 r r NOUN ejpam-587 170 2 c c NOUN ejpam-587 170 3 cδ cδ VERB ejpam-587 170 4 a a DET ejpam-587 170 5 b b PROPN ejpam-587 170 6 ( ( PUNCT ejpam-587 170 7 9 9 NUM ejpam-587 170 8 ) ) PUNCT ejpam-587 170 9 we we PRON ejpam-587 170 10 have have VERB ejpam-587 170 11 k k NOUN ejpam-587 170 12 = = PUNCT ejpam-587 171 1 r r NOUN ejpam-587 172 1 i i PRON ejpam-587 173 1 i i PRON ejpam-587 174 1 = = X ejpam-587 175 1 ra ra PROPN ejpam-587 176 1 a a DET ejpam-587 176 2 + + X ejpam-587 176 3 r r NOUN ejpam-587 176 4 â â X ejpam-587 176 5 â â X ejpam-587 176 6 = = SYM ejpam-587 176 7 2ra 2ra PROPN ejpam-587 176 8 a a PRON ejpam-587 176 9 . . PUNCT ejpam-587 177 1 thus thus ADV ejpam-587 177 2 r r NOUN ejpam-587 177 3 c c NOUN ejpam-587 177 4 c c NOUN ejpam-587 177 5 = = SYM ejpam-587 177 6 k k PROPN ejpam-587 177 7 2 2 NUM ejpam-587 178 1 so so SCONJ ejpam-587 178 2 the the DET ejpam-587 178 3 equation equation NOUN ejpam-587 178 4 ( ( PUNCT ejpam-587 178 5 9 9 X ejpam-587 178 6 ) ) PUNCT ejpam-587 178 7 becomes become VERB ejpam-587 178 8 : : PUNCT ejpam-587 178 9 ra ra PROPN ejpam-587 178 10 b b PROPN ejpam-587 178 11 = = SYM ejpam-587 178 12 k k PROPN ejpam-587 178 13 2n 2n NUM ejpam-587 178 14 δ δ PROPN ejpam-587 178 15 a a DET ejpam-587 178 16 b b X ejpam-587 178 17 k k PROPN ejpam-587 178 18 2n 2n PROPN ejpam-587 178 19 δ δ PROPN ejpam-587 178 20 â â X ejpam-587 178 21 b̂ b̂ NOUN ejpam-587 179 1 = = SYM ejpam-587 179 2 k k PROPN ejpam-587 179 3 2n 2n NUM ejpam-587 179 4 δ δ PROPN ejpam-587 179 5 a a DET ejpam-587 179 6 b b X ejpam-587 179 7 = = SYM ejpam-587 179 8 k k PROPN ejpam-587 179 9 2n 2n NUM ejpam-587 179 10 δ δ PROPN ejpam-587 180 1 a a DET ejpam-587 180 2 b b X ejpam-587 180 3 = = SYM ejpam-587 180 4 ra ra PROPN ejpam-587 180 5 b b PROPN ejpam-587 180 6 = = SYM ejpam-587 180 7 r r NOUN ejpam-587 180 8 â â X ejpam-587 180 9 b̂ b̂ NOUN ejpam-587 180 10 = = SYM ejpam-587 180 11 k k PROPN ejpam-587 180 12 2n 2n NUM ejpam-587 180 13 δ δ PROPN ejpam-587 180 14 â â X ejpam-587 180 15 b̂ b̂ NOUN ejpam-587 180 16 hence hence ADV ejpam-587 180 17 r r NOUN ejpam-587 180 18 i i PRON ejpam-587 180 19 j j NOUN ejpam-587 181 1 = = SYM ejpam-587 181 2 k k PROPN ejpam-587 181 3 2n 2n NUM ejpam-587 181 4 δ δ PROPN ejpam-587 182 1 i i PRON ejpam-587 182 2 j j VERB ejpam-587 182 3 therefore therefore ADV ejpam-587 182 4 , , PUNCT ejpam-587 182 5 from from ADP ejpam-587 182 6 [ [ X ejpam-587 182 7 13 13 NUM ejpam-587 182 8 ] ] PUNCT ejpam-587 182 9 m m VERB ejpam-587 182 10 is be AUX ejpam-587 182 11 einstein einstein PROPN ejpam-587 182 12 manifold manifold ADJ ejpam-587 182 13 with with ADP ejpam-587 182 14 cosmological cosmological ADJ ejpam-587 182 15 constant constant ADJ ejpam-587 182 16 k k PROPN ejpam-587 182 17 2n 2n NUM ejpam-587 182 18 . . PUNCT ejpam-587 183 1 references reference NOUN ejpam-587 183 2 736 736 NUM ejpam-587 183 3 references reference NOUN ejpam-587 183 4 [ [ X ejpam-587 183 5 1 1 NUM ejpam-587 183 6 ] ] PUNCT ejpam-587 183 7 a. a. PROPN ejpam-587 183 8 al al PROPN ejpam-587 183 9 - - PUNCT ejpam-587 183 10 otman otman PROPN ejpam-587 183 11 and and CCONJ ejpam-587 183 12 v. v. ADP ejpam-587 183 13 f. f. PROPN ejpam-587 183 14 kirichenko kirichenko PROPN ejpam-587 183 15 , , PUNCT ejpam-587 183 16 on on ADP ejpam-587 183 17 the the DET ejpam-587 183 18 geometry geometry NOUN ejpam-587 183 19 of of ADP ejpam-587 183 20 the the DET ejpam-587 183 21 bochner bochner NOUN ejpam-587 183 22 tensor tensor NOUN ejpam-587 183 23 of of ADP ejpam-587 183 24 nearly nearly ADV ejpam-587 183 25 kahler kahler NOUN ejpam-587 183 26 , , PUNCT ejpam-587 183 27 russian russian ADJ ejpam-587 183 28 mathematical mathematical ADJ ejpam-587 183 29 surveys survey NOUN ejpam-587 183 30 v.48 v.48 X ejpam-587 183 31 , , PUNCT ejpam-587 183 32 p.155 p.155 VERB ejpam-587 183 33 - - SYM ejpam-587 183 34 156 156 NUM ejpam-587 183 35 . . PUNCT ejpam-587 183 36 1993 1993 NUM ejpam-587 183 37 . . PUNCT ejpam-587 184 1 [ [ X ejpam-587 184 2 2 2 X ejpam-587 184 3 ] ] PUNCT ejpam-587 184 4 v. v. PROPN ejpam-587 184 5 i. i. PROPN ejpam-587 184 6 arnold arnold PROPN ejpam-587 184 7 , , PUNCT ejpam-587 184 8 mathematical mathematical ADJ ejpam-587 184 9 methods method NOUN ejpam-587 184 10 of of ADP ejpam-587 184 11 classical classical ADJ ejpam-587 184 12 mechanics mechanic NOUN ejpam-587 184 13 , , PUNCT ejpam-587 184 14 springer springer NOUN ejpam-587 184 15 . . PUNCT ejpam-587 184 16 1989 1989 NUM ejpam-587 184 17 . . PUNCT ejpam-587 185 1 [ [ X ejpam-587 185 2 3 3 X ejpam-587 185 3 ] ] X ejpam-587 185 4 s. s. PROPN ejpam-587 185 5 bochner bochner PROPN ejpam-587 185 6 , , PUNCT ejpam-587 185 7 curvature curvature NOUN ejpam-587 185 8 and and CCONJ ejpam-587 185 9 betti betti NOUN ejpam-587 185 10 numbers number NOUN ejpam-587 185 11 , , PUNCT ejpam-587 185 12 ii ii PROPN ejpam-587 185 13 , , PUNCT ejpam-587 185 14 ann ann PROPN ejpam-587 185 15 of of ADP ejpam-587 185 16 math math NOUN ejpam-587 185 17 . . PUNCT ejpam-587 185 18 , , PUNCT ejpam-587 185 19 v.50 v.50 X ejpam-587 185 20 , , PUNCT ejpam-587 185 21 p.77 p.77 NOUN ejpam-587 185 22 - - X ejpam-587 185 23 93 93 NUM ejpam-587 185 24 . . PUNCT ejpam-587 186 1 1949 1949 NUM ejpam-587 186 2 . . PUNCT ejpam-587 187 1 [ [ X ejpam-587 187 2 4 4 NUM ejpam-587 187 3 ] ] PUNCT ejpam-587 187 4 a. a. NOUN ejpam-587 187 5 gray gray NOUN ejpam-587 187 6 , , PUNCT ejpam-587 187 7 curvature curvature NOUN ejpam-587 187 8 identities identity NOUN ejpam-587 187 9 for for ADP ejpam-587 187 10 hermitian hermitian ADJ ejpam-587 187 11 and and CCONJ ejpam-587 187 12 almost almost ADV ejpam-587 187 13 hermitian hermitian ADJ ejpam-587 187 14 manifolds manifold NOUN ejpam-587 187 15 , , PUNCT ejpam-587 187 16 tohoku tohoku PROPN ejpam-587 187 17 math.j math.j NOUN ejpam-587 187 18 . . PUNCT ejpam-587 188 1 v. v. CCONJ ejpam-587 188 2 p.601 p.601 PROPN ejpam-587 188 3 - - PUNCT ejpam-587 188 4 612 612 NUM ejpam-587 188 5 . . PUNCT ejpam-587 188 6 1976 1976 NUM ejpam-587 188 7 . . PUNCT ejpam-587 189 1 [ [ X ejpam-587 189 2 5 5 X ejpam-587 189 3 ] ] PUNCT ejpam-587 189 4 v. v. PROPN ejpam-587 189 5 f. f. PROPN ejpam-587 189 6 kirichenko kirichenko PROPN ejpam-587 189 7 , , PUNCT ejpam-587 189 8 new new ADJ ejpam-587 189 9 results result NOUN ejpam-587 189 10 of of ADP ejpam-587 189 11 k k ADJ ejpam-587 189 12 - - PUNCT ejpam-587 189 13 spaces space NOUN ejpam-587 189 14 theory theory NOUN ejpam-587 189 15 , , PUNCT ejpam-587 189 16 ph.d.thesis ph.d.thesis PROPN ejpam-587 189 17 , , PUNCT ejpam-587 189 18 moscow moscow PROPN ejpam-587 189 19 state state PROPN ejpam-587 189 20 university university PROPN ejpam-587 189 21 . . PUNCT ejpam-587 190 1 1975 1975 NUM ejpam-587 190 2 . . PUNCT ejpam-587 191 1 [ [ X ejpam-587 191 2 6 6 NUM ejpam-587 191 3 ] ] PUNCT ejpam-587 191 4 v. v. PROPN ejpam-587 191 5 f. f. PROPN ejpam-587 191 6 kirichenko kirichenko PROPN ejpam-587 191 7 , , PUNCT ejpam-587 191 8 k k NOUN ejpam-587 191 9 - - PUNCT ejpam-587 191 10 spaces space NOUN ejpam-587 191 11 of of ADP ejpam-587 191 12 constant constant ADJ ejpam-587 191 13 type type NOUN ejpam-587 191 14 , , PUNCT ejpam-587 191 15 seper seper PROPN ejpam-587 191 16 . . PUNCT ejpam-587 191 17 math math PROPN ejpam-587 191 18 . . PUNCT ejpam-587 192 1 j. j. PROPN ejpam-587 192 2 v.17 v.17 PROPN ejpam-587 192 3 no.2 no.2 PROPN ejpam-587 192 4 , , PUNCT ejpam-587 192 5 p.282 p.282 NOUN ejpam-587 192 6 - - SYM ejpam-587 192 7 289 289 NUM ejpam-587 192 8 . . PUNCT ejpam-587 192 9 1976 1976 NUM ejpam-587 192 10 . . PUNCT ejpam-587 193 1 [ [ X ejpam-587 193 2 7 7 X ejpam-587 193 3 ] ] PUNCT ejpam-587 193 4 s. s. PROPN ejpam-587 193 5 kobayashi kobayashi PROPN ejpam-587 193 6 and and CCONJ ejpam-587 193 7 k. k. PROPN ejpam-587 193 8 nomizu nomizu PROPN ejpam-587 193 9 , , PUNCT ejpam-587 193 10 foundation foundation NOUN ejpam-587 193 11 of of ADP ejpam-587 193 12 differential differential ADJ ejpam-587 193 13 geometry geometry NOUN ejpam-587 193 14 , , PUNCT ejpam-587 193 15 v2 v2 PROPN ejpam-587 193 16 , , PUNCT ejpam-587 193 17 john john PROPN ejpam-587 193 18 wiley wiley PROPN ejpam-587 193 19 and and CCONJ ejpam-587 193 20 sons son NOUN ejpam-587 193 21 . . PUNCT ejpam-587 194 1 1969 1969 NUM ejpam-587 194 2 . . PUNCT ejpam-587 195 1 [ [ X ejpam-587 195 2 8 8 NUM ejpam-587 195 3 ] ] PUNCT ejpam-587 195 4 m. m. NOUN ejpam-587 195 5 mastumoto mastumoto NOUN ejpam-587 195 6 , , PUNCT ejpam-587 195 7 on on ADP ejpam-587 195 8 kahlerian kahlerian ADJ ejpam-587 195 9 spaces space NOUN ejpam-587 195 10 with with ADP ejpam-587 195 11 parallel parallel ADJ ejpam-587 195 12 or or CCONJ ejpam-587 195 13 vanishing vanish VERB ejpam-587 195 14 curvature curvature NOUN ejpam-587 195 15 tensor tensor NOUN ejpam-587 195 16 , , PUNCT ejpam-587 195 17 tensor tensor NOUN ejpam-587 195 18 , , PUNCT ejpam-587 195 19 n. n. PROPN ejpam-587 195 20 s. s. PROPN ejpam-587 195 21 v.20 v.20 PROPN ejpam-587 195 22 , , PUNCT ejpam-587 195 23 p. p. NOUN ejpam-587 195 24 25 25 NUM ejpam-587 195 25 - - SYM ejpam-587 195 26 28 28 NUM ejpam-587 195 27 . . PUNCT ejpam-587 195 28 1969 1969 NUM ejpam-587 195 29 . . PUNCT ejpam-587 196 1 [ [ X ejpam-587 196 2 9 9 NUM ejpam-587 196 3 ] ] PUNCT ejpam-587 196 4 k. k. PROPN ejpam-587 196 5 nam nam PROPN ejpam-587 196 6 , , PUNCT ejpam-587 196 7 note note VERB ejpam-587 196 8 on on ADP ejpam-587 196 9 kahlerian kahlerian ADJ ejpam-587 196 10 manifold manifold NOUN ejpam-587 196 11 whose whose DET ejpam-587 196 12 bochner bochner NOUN ejpam-587 196 13 curvature curvature NOUN ejpam-587 196 14 tensor tensor NOUN ejpam-587 196 15 vanishes vanish VERB ejpam-587 196 16 , , PUNCT ejpam-587 196 17 bull bull NOUN ejpam-587 196 18 . . PUNCT ejpam-587 197 1 korean korean ADJ ejpam-587 197 2 math math PROPN ejpam-587 197 3 . . PUNCT ejpam-587 198 1 soc soc PROPN ejpam-587 198 2 . . PROPN ejpam-587 198 3 , , PUNCT ejpam-587 198 4 25 25 NUM ejpam-587 198 5 , , PUNCT ejpam-587 198 6 no.1 no.1 NUM ejpam-587 198 7 , , PUNCT ejpam-587 198 8 p.99 p.99 NOUN ejpam-587 198 9 - - NOUN ejpam-587 198 10 105 105 NUM ejpam-587 198 11 . . PUNCT ejpam-587 198 12 1988 1988 NUM ejpam-587 198 13 . . PUNCT ejpam-587 199 1 [ [ X ejpam-587 199 2 10 10 NUM ejpam-587 199 3 ] ] PUNCT ejpam-587 199 4 z. z. PROPN ejpam-587 199 5 olsag olsag PROPN ejpam-587 199 6 , , PUNCT ejpam-587 199 7 bochner bochn ADJ ejpam-587 199 8 flat flat ADJ ejpam-587 199 9 manifolds manifold NOUN ejpam-587 199 10 , , PUNCT ejpam-587 199 11 diff diff PROPN ejpam-587 199 12 . . PUNCT ejpam-587 200 1 geom geom PROPN ejpam-587 200 2 .. .. PUNCT ejpam-587 200 3 banash banash PROPN ejpam-587 200 4 c. c. PROPN ejpam-587 200 5 p. p. PROPN ejpam-587 200 6 , , PUNCT ejpam-587 200 7 v.12 v.12 PROPN ejpam-587 200 8 , , PUNCT ejpam-587 200 9 p.219 p.219 NOUN ejpam-587 200 10 - - SYM ejpam-587 200 11 223 223 NUM ejpam-587 200 12 . . PUNCT ejpam-587 200 13 1984 1984 NUM ejpam-587 200 14 . . PUNCT ejpam-587 201 1 [ [ X ejpam-587 201 2 11 11 NUM ejpam-587 201 3 ] ] PUNCT ejpam-587 201 4 m. m. NOUN ejpam-587 201 5 petrovic petrovic PROPN ejpam-587 201 6 and and CCONJ ejpam-587 201 7 l. l. PROPN ejpam-587 201 8 vestraclen vestraclen PROPN ejpam-587 201 9 , , PUNCT ejpam-587 201 10 on on ADP ejpam-587 201 11 the the DET ejpam-587 201 12 concircular concircular ADJ ejpam-587 201 13 tensor tensor NOUN ejpam-587 201 14 , , PUNCT ejpam-587 201 15 the the DET ejpam-587 201 16 projective projective ADJ ejpam-587 201 17 curvature curvature NOUN ejpam-587 201 18 tensor tensor NOUN ejpam-587 201 19 of of ADP ejpam-587 201 20 bochner bochner NOUN ejpam-587 201 21 - - PUNCT ejpam-587 201 22 kahler kahler NOUN ejpam-587 201 23 manifolds manifold NOUN ejpam-587 201 24 , , PUNCT ejpam-587 201 25 math math NOUN ejpam-587 201 26 . . PUNCT ejpam-587 202 1 rep rep PROPN ejpam-587 202 2 . . PROPN ejpam-587 202 3 toyama toyama PROPN ejpam-587 202 4 univ univ PROPN ejpam-587 202 5 . . PROPN ejpam-587 202 6 , , PUNCT ejpam-587 202 7 v.10 v.10 ADP ejpam-587 202 8 , , PUNCT ejpam-587 202 9 p.37 p.37 NOUN ejpam-587 202 10 - - PUNCT ejpam-587 202 11 61 61 NUM ejpam-587 202 12 . . PUNCT ejpam-587 202 13 1987 1987 NUM ejpam-587 202 14 . . PUNCT ejpam-587 203 1 [ [ X ejpam-587 203 2 12 12 NUM ejpam-587 203 3 ] ] X ejpam-587 203 4 g. g. PROPN ejpam-587 203 5 b b PROPN ejpam-587 203 6 rizza rizza NOUN ejpam-587 203 7 , , PUNCT ejpam-587 203 8 varieta varieta NOUN ejpam-587 203 9 parakahleriane parakahleriane NOUN ejpam-587 203 10 , , PUNCT ejpam-587 203 11 ann ann PROPN ejpam-587 203 12 . . PROPN ejpam-587 203 13 math math PROPN ejpam-587 203 14 . . PUNCT ejpam-587 204 1 pura pura NOUN ejpam-587 204 2 et et PROPN ejpam-587 204 3 appl appl PROPN ejpam-587 205 1 . . PROPN ejpam-587 205 2 , , PUNCT ejpam-587 205 3 v.98 v.98 PROPN ejpam-587 205 4 , , PUNCT ejpam-587 205 5 no.4 no.4 PROPN ejpam-587 205 6 , , PUNCT ejpam-587 205 7 p.47 p.47 NOUN ejpam-587 205 8 - - X ejpam-587 205 9 61 61 NUM ejpam-587 205 10 . . PUNCT ejpam-587 205 11 1974 1974 NUM ejpam-587 205 12 . . PUNCT ejpam-587 206 1 [ [ X ejpam-587 206 2 13 13 NUM ejpam-587 206 3 ] ] PUNCT ejpam-587 206 4 m. m. NOUN ejpam-587 206 5 c. c. PROPN ejpam-587 206 6 sean sean PROPN ejpam-587 206 7 , , PUNCT ejpam-587 206 8 the the DET ejpam-587 206 9 cosmological cosmological ADJ ejpam-587 206 10 conatant conatant NOUN ejpam-587 206 11 , , PUNCT ejpam-587 206 12 irr irr PROPN ejpam-587 206 13 , , PUNCT ejpam-587 206 14 max max PROPN ejpam-587 206 15 - - PUNCT ejpam-587 206 16 planek planek NOUN ejpam-587 206 17 institut institut NOUN ejpam-587 206 18 fur fur NOUN ejpam-587 206 19 gravitations gravitation NOUN ejpam-587 206 20 physik physik NOUN ejpam-587 206 21 , , PUNCT ejpam-587 206 22 1 1 NUM ejpam-587 206 23 . . NUM ejpam-587 206 24 2001 2001 NUM ejpam-587 206 25 . . PUNCT ejpam-587 207 1 [ [ X ejpam-587 207 2 14 14 NUM ejpam-587 207 3 ] ] X ejpam-587 207 4 s. s. PROPN ejpam-587 207 5 tachibana tachibana PROPN ejpam-587 207 6 , , PUNCT ejpam-587 207 7 on on ADP ejpam-587 207 8 bochner bochner NOUN ejpam-587 207 9 curvature curvature NOUN ejpam-587 207 10 tensor tensor NOUN ejpam-587 207 11 , , PUNCT ejpam-587 207 12 not not PART ejpam-587 207 13 . . PUNCT ejpam-587 208 1 sci sci PROPN ejpam-587 208 2 . . PUNCT ejpam-587 208 3 ochanomidzu ochanomidzu PROPN ejpam-587 208 4 univ univ PROPN ejpam-587 208 5 . . PROPN ejpam-587 208 6 , , PUNCT ejpam-587 209 1 v.18 v.18 PROPN ejpam-587 209 2 , , PUNCT ejpam-587 209 3 p.15 p.15 PROPN ejpam-587 209 4 - - PUNCT ejpam-587 209 5 19 19 NUM ejpam-587 209 6 . . NOUN ejpam-587 209 7 1967 1967 NUM ejpam-587 209 8 . . PUNCT ejpam-587 210 1 [ [ X ejpam-587 210 2 15 15 NUM ejpam-587 210 3 ] ] X ejpam-587 210 4 s. s. PROPN ejpam-587 210 5 tachibana tachibana PROPN ejpam-587 210 6 , , PUNCT ejpam-587 210 7 notes note VERB ejpam-587 210 8 on on ADP ejpam-587 210 9 kahlerian kahlerian ADJ ejpam-587 210 10 metrics metric NOUN ejpam-587 210 11 with with ADP ejpam-587 210 12 vanishing vanish VERB ejpam-587 210 13 bochner bochner NOUN ejpam-587 210 14 curvature curvature NOUN ejpam-587 210 15 tensor tensor NOUN ejpam-587 210 16 , , PUNCT ejpam-587 210 17 kodi kodi PROPN ejpam-587 210 18 math math PROPN ejpam-587 210 19 . . PUNCT ejpam-587 211 1 semin semin PROPN ejpam-587 211 2 . . PUNCT ejpam-587 212 1 repts rept NOUN ejpam-587 212 2 . . PROPN ejpam-587 212 3 , , PUNCT ejpam-587 212 4 v.22 v.22 NOUN ejpam-587 212 5 , , PUNCT ejpam-587 212 6 p.313 p.313 NOUN ejpam-587 212 7 - - NOUN ejpam-587 212 8 321 321 NUM ejpam-587 212 9 . . PUNCT ejpam-587 212 10 1970 1970 NUM ejpam-587 212 11 . . PUNCT ejpam-587 213 1 [ [ X ejpam-587 213 2 16 16 NUM ejpam-587 213 3 ] ] X ejpam-587 213 4 e. e. PROPN ejpam-587 213 5 v. v. PROPN ejpam-587 213 6 tretiakova tretiakova PROPN ejpam-587 213 7 , , PUNCT ejpam-587 213 8 curvature curvature NOUN ejpam-587 213 9 identities identity NOUN ejpam-587 213 10 for for ADP ejpam-587 213 11 almost almost ADV ejpam-587 213 12 kahler kahler NOUN ejpam-587 213 13 manifold manifold ADJ ejpam-587 213 14 , , PUNCT ejpam-587 213 15 vinite vinite NOUN ejpam-587 213 16 , , PUNCT ejpam-587 213 17 moscow moscow PROPN ejpam-587 213 18 , , PUNCT ejpam-587 213 19 no.208 no.208 PROPN ejpam-587 213 20 - - PUNCT ejpam-587 213 21 b99 b99 NOUN ejpam-587 213 22 . . PUNCT ejpam-587 213 23 1999 1999 NUM ejpam-587 214 1 [ [ X ejpam-587 214 2 17 17 NUM ejpam-587 214 3 ] ] X ejpam-587 214 4 l. l. PROPN ejpam-587 214 5 vanhecke vanhecke PROPN ejpam-587 214 6 , , PUNCT ejpam-587 214 7 some some DET ejpam-587 214 8 almost almost ADV ejpam-587 214 9 hermitian hermitian ADJ ejpam-587 214 10 manifolds manifold NOUN ejpam-587 214 11 with with ADP ejpam-587 214 12 constant constant ADJ ejpam-587 214 13 holomorphic holomorphic ADJ ejpam-587 214 14 sectional sectional ADJ ejpam-587 214 15 curvature curvature NOUN ejpam-587 214 16 , , PUNCT ejpam-587 214 17 j. j. PROPN ejpam-587 214 18 diff diff PROPN ejpam-587 214 19 . . PUNCT ejpam-587 215 1 geom geom PROPN ejpam-587 215 2 . . PROPN ejpam-587 215 3 , , PUNCT ejpam-587 215 4 v.12 v.12 PROPN ejpam-587 215 5 , , PUNCT ejpam-587 215 6 no.4 no.4 PROPN ejpam-587 215 7 , , PUNCT ejpam-587 215 8 p.461 p.461 NOUN ejpam-587 215 9 - - PUNCT ejpam-587 215 10 467 467 NUM ejpam-587 215 11 . . PROPN ejpam-587 215 12 1977 1977 NUM ejpam-587 215 13 . . PUNCT ejpam-587 216 1 [ [ X ejpam-587 216 2 18 18 NUM ejpam-587 216 3 ] ] X ejpam-587 216 4 l. l. PROPN ejpam-587 216 5 vanhecke vanhecke PROPN ejpam-587 216 6 , , PUNCT ejpam-587 216 7 the the DET ejpam-587 216 8 bochner bochner NOUN ejpam-587 216 9 curvature curvature NOUN ejpam-587 216 10 tensor tensor NOUN ejpam-587 216 11 on on ADP ejpam-587 216 12 almost almost ADV ejpam-587 216 13 hermitian hermitian ADJ ejpam-587 216 14 manifold manifold ADJ ejpam-587 216 15 , , PUNCT ejpam-587 216 16 hokkaido hokkaido PROPN ejpam-587 216 17 math math PROPN ejpam-587 216 18 . . PUNCT ejpam-587 217 1 j. j. PROPN ejpam-587 217 2 , , PUNCT ejpam-587 217 3 v.7 v.7 PROPN ejpam-587 217 4 , , PUNCT ejpam-587 217 5 no.2 no.2 PROPN ejpam-587 217 6 , , PUNCT ejpam-587 217 7 p.252 p.252 NOUN ejpam-587 217 8 - - PUNCT ejpam-587 217 9 258 258 NUM ejpam-587 217 10 . . PUNCT ejpam-587 217 11 1987 1987 NUM ejpam-587 217 12 . . PUNCT