Nonnegatively curved fixed point homogeneous manifolds in low dimensions

Details Nonnegatively curved fixed point homogeneous manifolds in low dimensions Nonnegatively curved fixed point homogeneous manifolds in low dimensions

2009-11-06

arxiv.org/abs/0911.1254v3

Mathematics

Differential Geometry

To appear in Geom. Dedicata. Main difference with v1: "Linear" circle actions on $S^2\times S^2$ and $CP^2\#\pm CP^2$ are now

Scientific paper

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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