Nonnegatively curved fixed point homogeneous manifolds in low dimensions

Fernando Galaz-Garcia

Nonnegatively curved fixed point homogeneous manifolds in low dimensions

Differential Geometry 2011-06-13 v3

Authors: Fernando Galaz-Garcia

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.

Keywords

fixed-point homogeneous manifolds nonnegative curvature low dimensions compact Lie group action Riemannian manifolds classification

Cite

@article{arxiv.0911.1254,
  title  = {Nonnegatively curved fixed point homogeneous manifolds in low dimensions},
  author = {Fernando Galaz-Garcia},
  journal= {arXiv preprint arXiv:0911.1254},
  year   = {2011}
}

Comments

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 called "extendable actions". Typos corrected

Nonnegatively curved fixed point homogeneous manifolds in low dimensions

Abstract

Keywords

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