Nonnegatively curved fixed point homogeneous 5-manifolds
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- Galaz-Garcia, F. & Spindeler, W. Ann Glob Anal Geom (2012) 41: 253. doi:10.1007/s10455-011-9282-0
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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.