Preprint 18/2003

Metrics of positive Ricci curvature on quotient spaces

Lorenz J. Schwachhöfer and Wilderich Tuschmann

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Submission date: 20. Feb. 2003
Pages: 25
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We show that any closed biquotient with finite fundamental group admits a metric of positive Ricci curvature. Also, let (M,G) be a closed manifold with an action of cohomogeneity one, and let L be a closed subgroup of G which acts freely on M. We show that the quotient N := M/L carries metrics of nonnegative Ricci and almost nonnegative sectional curvature. Moreover, if N has finite fundamental group, we prove that N admits also metrics of positive Ricci curvature. Particular examples include infinite families of simply connected manifolds with the rational cohomology rings and integral homology of complex and quaternionic projective spaces.

07.06.2018, 02:10