Nonnegatively curved fixed point homogeneous manifolds in low dimensions

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.

To appear in Geom. Dedicata. Main difference with v1: "Linear" circle actions on $S^2\times S^2$ and $C{P}^2\#\pm C{P}^2$ are now called "extendable actions". Typos corrected

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• Developments around positive sectional curvature

Cited by in corpus (1)

• Nonnegatively curved fixed point homogeneous 5-manifolds