Highly connected 7-manifolds and non-negative sectional curvature

被引：13

作者：

Goette, S. ^{[1
]}

Kerin, M. ^{[2
]}

Shankar, K. ^{[3
]}

机构：

[1] Univ Freiburg, Math Inst, Freiburg, Germany

[2] NUI Galway, Sch Math Stat & Appl Math, Galway, Ireland

[3] Univ Oklahoma, Dept Math, Norman, OK 73019 USA

来源：

ANNALS OF MATHEMATICS | 2020年 / 191卷 / 03期

关键词：

highly connected 7-manifold; non-negative curvature; exotic sphere; Eells-Kuiper invariant; EQUIVARIANT ETA-INVARIANTS; EXOTIC SPHERES; CLASSIFICATION; MANIFOLDS; BIQUOTIENTS; S-3-BUNDLES; COHOMOLOGY;

D O I：

10.4007/annals.2020.191.3.3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, a six-parameter family of highly connected 7-manifolds which admit an SO(3)-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO(3)-invariant metric of non-negative curvature.

引用

页码：829 / 892

页数：64

共 50 条

[1] Einstein manifolds of non-negative sectional curvature and entropy
Paternain, GP
Petean, J
[J]. MATHEMATICAL RESEARCH LETTERS, 2000, 7 (04) : 503 - 515
[2] Certain 4-manifolds with non-negative sectional curvature
Cao, Jianguo
[J]. FRONTIERS OF MATHEMATICS IN CHINA, 2008, 3 (04) : 475 - 494
[3] Certain 4-manifolds with non-negative sectional curvature
Jianguo Cao
[J]. Frontiers of Mathematics in China, 2008, 3 : 475 - 494
[4] Torus manifolds and non-negative curvature
Wiemeler, Michael
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2015, 91 : 667 - 692
[5] ON COHOMOGENEITY ONE NONSIMPLY CONNECTED 7-MANIFOLDS OF CONSTANT POSITIVE CURVATURE
Zarei, M.
Kashani, S. M. B.
Abedi, H.
[J]. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2016, 42 (03): : 565 - 584
[6] SOME NONDIFFEOMORPHIC HOMEOMORPHIC HOMOGENEOUS 7-MANIFOLDS WITH POSITIVE SECTIONAL CURVATURE
KRECK, M
STOLZ, S
[J]. JOURNAL OF DIFFERENTIAL GEOMETRY, 1991, 33 (02) : 465 - 486
[7] THE HERMITIAN CURVATURE FLOW ON MANIFOLDS WITH NON-NEGATIVE GRIFFITHS CURVATURE
Ustinovskiy, Yury
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2019, 141 (06) : 1751 - 1775
[8] Complete submanifolds in manifolds of partially non-negative curvature
Qiaoling Wang
[J]. Annals of Global Analysis and Geometry, 2010, 37 : 113 - 124
[9] Complete submanifolds in manifolds of partially non-negative curvature
Wang, Qiaoling
[J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2010, 37 (02) : 113 - 124
[10] On manifolds with non-negative Ricci curvature and Sobolev inequalities
Ledoux, M
[J]. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 1999, 7 (02) : 347 - 353

← 1 2 3 4 5 →