New Examples of Obstructions to Non-Negative Sectional Curvatures in Cohomogeneity One Manifolds

Details New Examples of Obstructions to Non-Negative Sectional Curvatures in Cohomogeneity One Manifolds New Examples of Obstructions to Non-Negative Sectional Curvatures in Cohomogeneity One Manifolds

2009-10-29

arxiv.org/abs/0910.5712v1

Mathematics

Differential Geometry

44 pages, 4 tables and one appendix

Scientific paper

K. Grove, L. Verdiani, B. Wilking and W. Ziller gave the first examples of
cohomogeneity one manifolds which do not carry invariant metrics with
non-negative sectional curvatures. In this paper we generalize their results to
a larger family. We also classified all class one representations for a pair
(G;H) with G/H some sphere, which are used to construct the examples.

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