AN EXOTIC T1S4 WITH POSITIVE CURVATURE

被引：1

作者：

Grove, Karsten ^{[1
]}

Verdiani, Luigi ^{[2
]}

Ziller, Wolfgang ^{[3
]}

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] Dipartimento Matemat Applicata, I-50139 Florence, Italy

[3] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2011年 / 21卷 / 03期

基金：

美国国家科学基金会;

关键词：

Positive curvature; connection metrics; cohomogeneity one; 3-Sasakian manifolds; COHOMOGENEITY ONE MANIFOLDS; RIEMANNIAN-MANIFOLDS; EVEN DIMENSION; CLASSIFICATION; EXAMPLES;

D O I：

10.1007/s00039-011-0117-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a metric with positive sectional curvature on a 7-manifold which supports an isometry group with orbits of codimension 1. It is a connection metric on the total space of an orbifold 3-sphere bundle over an orbifold 4-sphere. By a result of S. Goette, the manifold is homeomorphic but not diffeomorphic to the unit tangent bundle of the 4-sphere.

引用

页码：499 / 524

页数：26

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