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Nonnegatively curved fixed point homogeneous manifolds in low dimensions. [Preprint]

Galaz-Garcia, Fernando

Abstract:
Let G be a compact Lie group acting isometrically on a compact Riemannian manifold M with nonempty fixed point set MG. We say that M is fixed-point homogeneous if G acts transitively on a normal sphere to some component of MG. Fixed-point homogeneous manifolds with positive sectional curvature have been completely classified. We classify fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected 4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure.


Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Buchaufsatz
Jahr 2009
Sprache Englisch
Identifikator KITopen ID: 1000051171
Erschienen in arXiv [math.DG]
Seiten arXiv:0911.1254
URLs http://arxiv.org/abs/0911.1254
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