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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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The Splitting Theorem and topology of noncompact spaces with nonnegative N-Bakry Émery Ricci curvature
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by Alice Lim PDF
Proc. Amer. Math. Soc. 149 (2021), 3515-3529 Request permission

Abstract:

In this paper, we generalize topological results known for noncompact manifolds with nonnegative Ricci curvature to spaces with nonnegative $N$-Bakry Émery Ricci curvature. We study the Splitting Theorem and a property called the geodesic loops to infinity property in relation to spaces with nonnegative $N$-Bakry Émery Ricci curvature. In addition, we show that if $M^n$ is a complete, noncompact Riemannian manifold with nonnegative $N$-Bakry Émery Ricci curvature where $N>n$, then $H_{n-1}(M,\mathbb {Z})$ is $0$.
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Additional Information
  • Alice Lim
  • Affiliation: Department of Mathematics, Syracuse University, 215 Carnegie Building, Syracuse, New York 13244
  • Email: awlim100@syr.edu
  • Received by editor(s): April 22, 2020
  • Received by editor(s) in revised form: June 15, 2020
  • Published electronically: May 12, 2021
  • Additional Notes: This work was partially supported by NSF grant DMS-1654034.
  • Communicated by: Jia-Ping Wang
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 3515-3529
  • MSC (2020): Primary 53C20
  • DOI: https://doi.org/10.1090/proc/15240
  • MathSciNet review: 4273153