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Metrics of positive Ricci curvature on quotient spaces
Lorenz J. Schwachhöfer and Wilderich Tuschmann
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.