Positively Curved Cohomogeneity One Manifolds and 3-Sasakian Geometry

Details Positively Curved Cohomogeneity One Manifolds and 3-Sasakian Geometry Positively Curved Cohomogeneity One Manifolds and 3-Sasakian Geometry

2005-11-18

arxiv.org/abs/math/0511464v3

Mathematics

Differential Geometry

minor corrections and additions and change in title

Scientific paper

We give an exhaustive description of all simply connected odd dimensional cohomogeneity one manifolds that can possibly support an invariant metric with positive sectional curvature. Among the known examples of odd dimensional manifolds with positive curvature, apart from spheres, there are two infinite families among the 7-dimensional Eschenburg spaces and 13-dimensional Bazaikin spaces and one isolated 7-dimensional Berger space with this property. In addition to these examples, it turns out that only one isolated 7-manifold, and two infinite 7-dimensional families, potentially admit invariant cohomogeneity one metrics of positive curvature.

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