Almost nonnegative curvature operator and cohomology rings

被引：0

作者：

Herrmann, Martin ^{[1
,2
]}

机构：

[1] Karlsruher Inst Technol, Fak Math, Kaiserstr 89-93, D-76133 Karlsruhe, Germany

[2] Univ Munster, Math Inst, Einsteinstr 62, D-48149 Munster, Germany

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2016年 / 11卷 / 05期

关键词：

Nonnegative curvature; homogeneous spaces; curvature operator; almost nonnegative curvature; COMPACT KAHLER-MANIFOLDS; POSITIVE CURVATURE; DIFFEOMORPHISM FINITENESS; FUNDAMENTAL-GROUPS; SPLITTING THEOREM; CURVED MANIFOLDS; DIAMETER; HOMOTOPY; SPACES; BUNDLES;

D O I：

10.1007/s11464-016-0569-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a survey of results on the construction of and obstructions to metrics of almost nonnegative curvature operator on closed manifolds and results on the cohomology rings of closed, simply-connected manifolds with a lower curvature and upper diameter bound. The latter is motivated by a question of Grove whether these condition imply finiteness of rational homotopy types. This question has answers by F. Fang-X. Rong, B. Totaro and recently A. Dessai and the present author.

引用

页码：1259 / 1274

页数：16

共 45 条

[1] INFINITE FAMILY OF DISTINCT 7-MANIFOLDS ADMITTING POSITIVELY CURVED RIEMANNIAN STRUCTURES [J].