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Riemannian submersions need not preserve positive Ricci curvature


Authors: Curtis Pro and Frederick Wilhelm
Journal: Proc. Amer. Math. Soc. 142 (2014), 2529-2535
MSC (2010): Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-2014-11960-5
Published electronically: April 4, 2014
MathSciNet review: 3195773
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Abstract | References | Similar Articles | Additional Information

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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References
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Additional Information

Curtis Pro
Affiliation: Department of Mathematics, University of California, Riverside, Riverside, California 92521
Address at time of publication: Department of Mathematics, University of Toronto, Toronto, ON, Canada M5S 2E4
Email: cpro@math.toronto.edu

Frederick Wilhelm
Affiliation: Department of Mathematics, University of California, Riverside, Riverside, California 92521

Received by editor(s): June 17, 2012
Received by editor(s) in revised form: July 12, 2012
Published electronically: April 4, 2014
Communicated by: Lei Ni
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.