Metrics of positive Ricci curvature on quotient spaces

Details Metrics of positive Ricci curvature on quotient spaces Metrics of positive Ricci curvature on quotient spaces

2003-03-07

arxiv.org/abs/math/0303092v1

Mathematics

Differential Geometry

23 pages

Scientific paper

We show that any closed biquotient with finite fundamental group admits metrics of positive Ricci curvature. Also, let M be a closed manifold on which a compact Lie group G acts with 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, then 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.

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