Polar actions with a fixed point

We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar and the section is the tangent space of an embedded totally...

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Bibliographic Details
Published inDifferential geometry and its applications Vol. 29; no. 1; pp. 20 - 25
Main Authors Díaz-Ramos, J.C., Kollross, A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2011
Subjects
Classification
Criteria
Differential geometry
Lie groups
Manifolds
Mathematics
Polar action
Representations
Symmetric space
Tangents
57S15
Polar action
53C35
Symmetric space
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Summary:We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar and the section is the tangent space of an embedded totally geodesic submanifold. We apply this to obtain a classification of polar actions with a fixed point on symmetric spaces.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2011.01.001