Nonnegatively curved fixed point homogeneous 5-manifolds

2011/05/03 by Galaz-Garcia, Fernando, Spindeler, Wolfgang
#53C20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1105.0551

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 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.

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