Classification of Cohomogeneity One Manifolds in Low Dimensions

Details Classification of Cohomogeneity One Manifolds in Low Dimensions Classification of Cohomogeneity One Manifolds in Low Dimensions

2007-12-09

arxiv.org/abs/0712.1327v1

Mathematics

Differential Geometry

Scientific paper

A cohomogeneity one manifold is a manifold with the action of a compact Lie group, whose quotient is one dimensional. Such manifolds are of interest in Riemannian geometry, in the context of nonnegative sectional curvature, as well as in other areas of geometry and in physics. In this paper we classify compact simply connected cohomogeneity one manifolds in dimensions 5, 6 and 7. We also show that all such manifolds admit metrics of nonnegative sectional curvature, with the possible exception of two families of manifolds.

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