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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Riemannian submersions need not preserve positive Ricci curvature
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by Curtis Pro and Frederick Wilhelm PDF
Proc. Amer. Math. Soc. 142 (2014), 2529-2535 Request permission

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.
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
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 2529-2535
  • MSC (2010): Primary 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-2014-11960-5
  • MathSciNet review: 3195773