id sid eid entity type cana-590 1 1 1074 CARDINAL cana-590 1 2 31 CARDINAL cana-590 2 1 2s CARDINAL cana-590 2 2 2024 CARDINAL cana-590 2 3 26 CARDINAL cana-590 2 4 grassmannian ORG cana-590 2 5 1 CARDINAL cana-590 2 6 shruti kamalakar PERSON cana-590 2 7 2 1department DATE cana-590 2 8 mathematical sciences institute ORG cana-590 2 9 karnataka GPE cana-590 2 10 india GPE cana-590 3 1 2department TIME cana-590 3 2 rani channamma university PERSON cana-590 3 3 karnataka GPE cana-590 3 4 india e GPE cana-590 3 5 26-02-2024 CARDINAL cana-590 3 6 28-04-2024 CARDINAL cana-590 3 7 12-05-2024 CARDINAL cana-590 3 8 manifolds ORG cana-590 3 9 manifolds ORG cana-590 4 1 manifolds ORG cana-590 5 1 1 CARDINAL cana-590 5 2 manifolds ORG cana-590 7 1 grassmannians NORP cana-590 8 1 grassmannians NORP cana-590 9 1 1.1 CARDINAL cana-590 9 2 𝐢𝑛that GPE cana-590 9 3 k-plane 𝐴. PERSON cana-590 9 4 k. PERSON cana-590 10 1 𝐴 and 𝐴' ORG cana-590 10 2 two CARDINAL cana-590 11 1 1 CARDINAL cana-590 12 1 𝐢n ORG cana-590 12 2 𝑗 βˆ‰ 𝐼 PERSON cana-590 13 1 2 CARDINAL cana-590 13 2 manifolds ORG cana-590 14 1 2.1 CARDINAL cana-590 15 1 πœ‘π›Όπ‘œπœ‘π›½ -1 ORG cana-590 15 2 ∩ π‘ˆπ›½ PERSON cana-590 15 3 1074 CARDINAL cana-590 15 4 31 CARDINAL cana-590 16 1 2s CARDINAL cana-590 16 2 2024 CARDINAL cana-590 16 3 27 CARDINAL cana-590 16 4 π‘ˆπ›Ό ∩ ORG cana-590 17 1 ↓ ↓ ORG cana-590 17 2 -1 ORG cana-590 17 3 𝐢nβŠƒ DATE cana-590 17 4 2.2 CARDINAL cana-590 17 5 π‘ˆ βŠ‚ 𝑀 ORG cana-590 17 6 π‘“π‘œπœ‘π›Ό -1 ORG cana-590 18 1 π‘ˆ βŠ‚ 𝑀 ORG cana-590 18 2 -1 ORG cana-590 18 3 𝑧(π‘ˆβ‹‚π‘ˆπ›Ό ORG cana-590 18 4 2.3 CARDINAL cana-590 18 5 𝑁. NORP cana-590 18 6 one CARDINAL cana-590 19 1 𝑃𝑛. NORP cana-590 21 1 πœ‘π‘–([𝑧0 ORG cana-590 32 1 β„™1 PRODUCT cana-590 35 1 2plane CARDINAL cana-590 37 1 2.4 CARDINAL cana-590 38 1 πœ‹βˆ’1(𝑝𝑖 ORG cana-590 39 1 2.5 CARDINAL cana-590 39 2 0 CARDINAL cana-590 39 3 zero CARDINAL cana-590 40 1 1074 CARDINAL cana-590 40 2 31 CARDINAL cana-590 41 1 2s CARDINAL cana-590 41 2 2024 CARDINAL cana-590 41 3 28 CARDINAL cana-590 43 1 1 CARDINAL cana-590 44 1 𝐢n GPE cana-590 44 2 𝐢n ORG cana-590 44 3 2𝑛 CARDINAL cana-590 44 4 πΆβˆ—/𝛬 PERSON cana-590 45 1 πœ‹ PERSON cana-590 47 1 3 CARDINAL cana-590 48 1 three CARDINAL cana-590 49 1 2𝑛. CARDINAL cana-590 51 1 πœ•π‘¦π‘– CARDINAL cana-590 52 1 𝐢∞ GPE cana-590 53 1 πœ•π‘¦π‘– CARDINAL cana-590 53 2 βŠ‚ GPE cana-590 54 1 1074 CARDINAL cana-590 54 2 31 CARDINAL cana-590 55 1 2s CARDINAL cana-590 55 2 2024 CARDINAL cana-590 55 3 29 CARDINAL cana-590 58 1 βŠ‚ GPE cana-590 59 1 𝑇𝑅 ORG cana-590 60 1 ⟢ CARDINAL cana-590 62 1 3.1 CARDINAL cana-590 62 2 𝑧(𝑑 ORG cana-590 62 3 0 ≀ 𝑑 ≀ MONEY cana-590 63 1 𝑧(𝑑 ORG cana-590 63 2 πœ•π‘₯ + 𝑦′(t DATE cana-590 63 3 πœ•π‘§ CARDINAL cana-590 63 4 two CARDINAL cana-590 69 1 𝑓(𝑝 PERSON cana-590 70 1 4 CARDINAL cana-590 70 2 manifolds ORG cana-590 70 3 4.1 CARDINAL cana-590 70 4 𝑓1 ORG cana-590 73 1 zeros CARDINAL cana-590 74 1 0 CARDINAL cana-590 74 2 1 CARDINAL cana-590 75 1 1074 CARDINAL cana-590 75 2 31 CARDINAL cana-590 76 1 2s CARDINAL cana-590 76 2 2024 CARDINAL cana-590 76 3 30 DATE cana-590 80 1 4.2 CARDINAL cana-590 80 2 grassmannians NORP cana-590 80 3 manifolds ORG cana-590 83 1 affine ORG cana-590 85 1 5 CARDINAL cana-590 85 2 abelian NORP cana-590 86 1 one CARDINAL cana-590 91 1 5.1 CARDINAL cana-590 92 1 two CARDINAL cana-590 94 1 𝑅𝑛 PERSON cana-590 98 1 grassmannians NORP cana-590 104 1 two CARDINAL cana-590 104 2 𝐴 ORG cana-590 105 1 𝑔. 𝐡. PERSON cana-590 106 1 1074 CARDINAL cana-590 106 2 31 CARDINAL cana-590 107 1 2s CARDINAL cana-590 107 2 2024 CARDINAL cana-590 109 1 𝑅2 CARDINAL cana-590 113 1 6 CARDINAL cana-590 113 2 𝑅2 CARDINAL cana-590 113 3 𝑅3 CARDINAL cana-590 114 1 two CARDINAL cana-590 115 1 𝑅2 CARDINAL cana-590 116 1 1 CARDINAL cana-590 116 2 algebraic geometry PERSON cana-590 116 3 first ORDINAL cana-590 117 1 lakshmibai ORG cana-590 118 1 2 CARDINAL cana-590 118 2 hatcher PERSON cana-590 118 3 allen PERSON cana-590 118 4 2003).vector CARDINAL cana-590 119 1 3 CARDINAL cana-590 119 2 jeanpierre serre PERSON cana-590 119 3 berlin GPE cana-590 119 4 2003 DATE cana-590 120 1 4 CARDINAL cana-590 120 2 peter buser PERSON cana-590 120 3 vol.106,birkhouser boston,inc. ORG cana-590 120 4 11833224 DATE cana-590 121 1 5 CARDINAL cana-590 121 2 arym mirza khani PERSON cana-590 121 3 bram petri ORG cana-590 121 4 comment.math.helv PERSON cana-590 123 1 6 CARDINAL cana-590 123 2 thomas bendokat PERSON cana-590 123 3 ralf zimmermann PERSON cana-590 125 1 7 CARDINAL cana-590 125 2 r. mahony PERSON cana-590 125 3 r. sepulchre PERSON cana-590 126 1 riemannian NORP cana-590 126 2 grassmann manifolds ORG cana-590 127 1 mathematica PERSON cana-590 127 2 80(2):199–220, 2004 DATE cana-590 128 1 8 CARDINAL cana-590 128 2 a. a. borisenko PERSON cana-590 128 3 yu. a. nikolaevski˘ı PERSON cana-590 128 4 grassmann manifolds ORG cana-590 129 1 46(2(278)):41–83 CARDINAL cana-590 129 2 240 CARDINAL cana-590 129 3 1991 DATE cana-590 130 1 9 CARDINAL cana-590 130 2 j. m. lee PERSON cana-590 130 3 smooth manifolds ORG cana-590 132 1 new york GPE cana-590 132 2 2012 DATE cana-590 133 1 10 CARDINAL cana-590 133 2 a. machado PERSON cana-590 133 3 i. salavessa PERSON cana-590 134 1 grassmannian manifolds ORG cana-590 135 1 santiago de compostela ORG cana-590 135 2 1984 DATE cana-590 135 3 131 CARDINAL cana-590 137 1 85–102 CARDINAL cana-590 137 2 pitman GPE cana-590 137 3 boston GPE cana-590 137 4 ma GPE cana-590 137 5 1985 DATE cana-590 138 1 11 CARDINAL cana-590 138 2 l. qiu GPE cana-590 138 3 y. zhang PERSON cana-590 139 1 li PERSON cana-590 140 1 siam journal ORG cana-590 140 2 27(2):507–25, 2005 DATE