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New examples of obstructions to non-negative sectional curvatures in cohomogeneity one manifolds


Author: Chenxu He
Journal: Trans. Amer. Math. Soc. 366 (2014), 6093-6118
MSC (2010): Primary 53C20, 53C30
DOI: https://doi.org/10.1090/S0002-9947-2014-06194-1
Published electronically: March 4, 2014
MathSciNet review: 3256194
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Abstract: 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 classify all class one representations for a pair $ (G,H)$ with $ G/H$ a sphere, which are used to construct the examples.


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Additional Information

Chenxu He
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Address at time of publication: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: che@math.ou.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06194-1
Received by editor(s): June 21, 2012
Received by editor(s) in revised form: April 8, 2013
Published electronically: March 4, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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