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Almost Nonnegative Curvature and Cohomogeneity One

Schwachhöfer, Lorenz J.; Tuschmann, Wilderich

Abstract: We show that any close cohomogeneity one manifold supports metrics of almost non­-negative sectional curvature which are moreover invariant under the cohomogeneity one action, thereby establishing a conjecture of Grove and Ziller in the almost nonnegatively curved setting. Applications of our result include that there are infinitely many dimensions in which there exist almost nonnegatively curved topological spheres and homotopy lens as well as homotopy real projective spaces, all differentiably distinct from the standard ones.

Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Buchaufsatz
Jahr 2001
Sprache Englisch
Identifikator KITopen ID: 1000047148
Erschienen in Curvature and Cohomogeneity One. Ed.: L. Schwachhöfer
Verlag Leipzig
Seiten 1-24
Serie Max-Planck-Institut für Mathematik in den Natuwissenschaften, Leipzig / Preprint ; 62
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