Theorems of Barth-Lefschetz type and Morse theory on the space of paths in homogeneous spaces

被引：0

作者：

Senapathi, Chaitanya ^{[1
]}

机构：

[1] Tata Inst Fundamental Res, Mumbai, Maharashtra, India

来源：

GEOMETRIAE DEDICATA | 2015年 / 178卷 / 01期

关键词：

Flag varieties; Morse theory; Path space; Homotopy connectedness; Non-negative curvature; Canonical connection; COMPLEX SUBSPACES; KAHLER-MANIFOLDS; HOMOTOPY-GROUPS; CONNECTEDNESS;

D O I：

10.1007/s10711-015-0053-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Homotopy connectedness theorems for complex submanifolds of homogeneous spaces (sometimes referred to as theorems of Barth-Lefshetz type) have been established by a number of authors. Morse theory on the space of paths lead to an elegant proof of homotopy connectedness theorems for complex submanifolds of Hermitian symmetric spaces. In this work we extend this proof to a larger class of compact complex homogeneous spaces.

引用

页码：195 / 217

页数：23

共 50 条

[1] Theorems of Barth-Lefschetz type and Morse theory on the space of paths in homogeneous spaces
Chaitanya Senapathi
[J]. Geometriae Dedicata, 2015, 178 : 195 - 217
[2] Theorems of Barth-Lefschetz type and Morse theory on the space of paths
Schoen, R
Wolfson, J
[J]. MATHEMATISCHE ZEITSCHRIFT, 1998, 229 (01) : 77 - 89
[3] Theorems of Barth-Lefschetz type and Morse theory on the space of paths
Richard Schoen
Jon Wolfson
[J]. Mathematische Zeitschrift, 1998, 229 : 77 - 89
[4] BARTH-LEFSCHETZ THEOREMS FOR SINGULAR SPACES
OKONEK, C
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1987, 374 : 24 - 38
[5] THEOREMS OF BARTH-LEFSCHETZ TYPE FOR COMPLEX SUBSPACES OF HOMOGENEOUS COMPLEX MANIFOLDS
SOMMESE, AJ
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1977, 74 (04) : 1332 - 1333
[6] Theorems of Barth-Lefschetz type in Sasakian geometry
Chen, Xiaoyang
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2015, 38 : 114 - 123
[7] Algebraic Barth-Lefschetz theorems
Badescu, L
[J]. NAGOYA MATHEMATICAL JOURNAL, 1996, 142 : 17 - 38
[8] THEOREMS OF BARTH-LEFSCHETZ TYPE ON KAHLER MANIFOLDS WITH PARTIALLY POSITIVE CURVATURE
ZHOU DETANG Insitituto de Matematica
[J]. Chinese Annals of Mathematics, 2003, (03) : 285 - 292
[9] Theorems of Barth-Lefschetz type on Kahler manifolds with partially positive curvature
Zhou, DT
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2003, 24 (03): : 285 - 292
[10] A BARTH-LEFSCHETZ THEOREM FOR SUBMANIFOLDS OF A PRODUCT OF PROJECTIVE SPACES
Badescu, Lucian
Repetto, Flavia
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2009, 20 (01) : 77 - 96

← 1 2 3 4 5 →