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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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Asymptotically cylindrical Ricci-flat manifolds
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by Sema Salur PDF
Proc. Amer. Math. Soc. 134 (2006), 3049-3056 Request permission

Abstract:

Asymptotically cylindrical Ricci-flat manifolds play a key role in constructing Topological Quantum Field Theories. It is particularly important to understand their behavior at the cylindrical ends and the natural restrictions on the geometry. In this paper we show that an orientable, connected, asymptotically cylindrical manifold $(M,g)$ with Ricci-flat metric $g$ can have at most two cylindrical ends. In the case where there are two such cylindrical ends, then there is reduction in the holonomy group Hol$(g)$ and $(M,g)$ is a cylinder.
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Additional Information
  • Sema Salur
  • Affiliation: Department of Mathematics, Northwestern University, Evanston, Illiinois 60208
  • Email: salur@math.northwestern.edu
  • Received by editor(s): November 17, 2004
  • Received by editor(s) in revised form: April 7, 2005, and April 26, 2005
  • Published electronically: April 13, 2006
  • Additional Notes: This research was supported in part by AWM-NSF Mentoring grant
  • Communicated by: Richard A. Wentworth
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3049-3056
  • MSC (2000): Primary 53C15, 53C21; Secondary 58J05
  • DOI: https://doi.org/10.1090/S0002-9939-06-08313-4
  • MathSciNet review: 2231631