

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
Bibtex
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Abstract:
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.