Polar manifolds and actions

被引：23

作者：

Grove, Karsten ^{[1
]}

Ziller, Wolfgang ^{[2
]}

机构：

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

[2] Univ Penn, Philadelphia, PA 19104 USA

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2012年 / 11卷 / 02期

基金：

美国国家科学基金会;

关键词：

Group actions; sections; rationally elliptic; COHOMOGENEITY ONE MANIFOLDS; RIEMANNIAN FOLIATIONS; EVEN DIMENSION; CURVATURE; CLASSIFICATION; HYPERPOLAR; SPHERES;

D O I：

10.1007/s11784-012-0087-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A group action is called polar if there exists an immersed submanifold (a section) which intersects all orbits orthogonally. We show how to construct a manifold admitting a polar group action by prescribing its isotropy groups along a fundamental domain in the section. This generalizes a classical construction for cohomogeneity-one manifolds.We give many examples showing the richness of this class of group actions and relate the topology of the section to the topology of the manifold.

引用

页码：279 / 313

页数：35

共 70 条

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