Riemannian Submersions Need Not Preserve Positive Ricci Curvature

Curtis Pro; Frederick Wilhelm

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arXiv · 1206.3766

Riemannian Submersions Need Not Preserve Positive Ricci Curvature

Curtis Pro·Frederick Wilhelm

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Abstract

If $\pi :M\rightarrow B$ is a Riemannian Submersion and $M$ has positive sectional curvature, O'Neill's Horizontal Curvature Equation shows that $B$ must also have positive curvature. We show there are Riemannian submersions from compact manifolds with positive Ricci curvature to manifolds that have small neighborhoods of (arbitrarily) negative Ricci curvature, but that there are no Riemannian submersions from manifolds with positive Ricci curvature to manifolds with nonpositive Ricci curvature.

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Curtis Pro, Frederick Wilhelm. 2012-06-17. Riemannian Submersions Need Not Preserve Positive Ricci Curvature. https://arxiv.org/abs/1206.3766

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