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arXiv · 0911.1254

Nonnegatively curved fixed point homogeneous manifolds in low dimensions

Fernando Galaz-Garcia
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Abstract

Let $G$ be a compact Lie group acting isometrically on a compact Riemannian manifold $M$ with nonempty fixed point set $M^G$. We say that $M$ is fixed-point homogeneous if $G$ acts transitively on a normal sphere to some component of $M^G$. 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.

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Fernando Galaz-Garcia. 2009-11-06. Nonnegatively curved fixed point homogeneous manifolds in low dimensions. https://arxiv.org/abs/0911.1254

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