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 7 is reduced to only one further family of candidates
Seven dimensional cohomogeneity one manifolds with nonnegative curvature / Verdiani, Luigi. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 371:(2018), pp. 655-662. [10.1007/s00208-017-1618-z]
Seven dimensional cohomogeneity one manifolds with nonnegative curvature
VERDIANI, LUIGI
2018
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 7 is reduced to only one further family of candidates
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