Nonnegatively curved fixed point homogeneous 5-manifolds
Abstract
Let $G$ be a compact Lie group acting effectively by isometries on a compact Riemannian manifold $M$ with nonempty fixed point set $Fix(M,G)$. We say that the action is \emph{fixed point homogeneous} if $G$ acts transitively on a normal sphere to some component of $Fix(M,G)$, equivalently, if $Fix(M,G)$ has codimension one in the orbit space of the action. We classify up to diffeomorphism closed, simply connected 5-manifolds with nonnegative sectional curvature and an effective fixed point homogeneous isometric action of a compact Lie group.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2011
- DOI:
- 10.48550/arXiv.1105.0551
- arXiv:
- arXiv:1105.0551
- Bibcode:
- 2011arXiv1105.0551G
- Keywords:
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- Mathematics - Differential Geometry;
- 53C20
- E-Print:
- 12 pages