Positively Curved Cohomogeneity One Manifolds and 3-Sasakian Geometry
Differential Geometry
2007-05-23 v3
Abstract
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.
Keywords
Cite
@article{arxiv.math/0511464,
title = {Positively Curved Cohomogeneity One Manifolds and 3-Sasakian Geometry},
author = {K. Grove and B. Wilking and W. Ziller},
journal= {arXiv preprint arXiv:math/0511464},
year = {2007}
}
Comments
minor corrections and additions and change in title