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.
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页码：499 / 524
页数：26
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