Abstract
We show that a certain family of cohomogeneity one manifolds does not admit an invariant metric of nonnegative sectional curvature, unless it admits one with positive curvature. As a consequence, the classification of nonnegatively curved cohomogeneity one manifolds in dimension seven is reduced to only one further family of candidates.
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Communicated by F. C. Marques.
Luigi Verdiani was supported by the University of Pennsylvania and would like to thank the Institute for its hospitality. Wolfgang Ziller was supported by a grant from the National Science Foundation.
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Verdiani, L., Ziller, W. Seven dimensional cohomogeneity one manifolds with nonnegative curvature. Math. Ann. 371, 655–662 (2018). https://doi.org/10.1007/s00208-017-1618-z
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DOI: https://doi.org/10.1007/s00208-017-1618-z