Cohomogeneity one manifolds with a small family of invariant metrics

Details Cohomogeneity one manifolds with a small family of invariant metrics Cohomogeneity one manifolds with a small family of invariant metrics

2010-06-02

arxiv.org/abs/1006.0438v1

Mathematics

Differential Geometry

64 pages, 2 appendices and 19 tables

Scientific paper

In this paper, we classify compact simply connected cohomogeneity one manifolds up to equivariant diffeomorphism whose isotropy representation by the connected component of the principal isotropy subgroup has three or less irreducible summands. The manifold is either a bundle over a homogeneous space or an irreducible symmetric space. As a corollary such manifolds admit an invariant metric with non-negative sectional curvature.

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