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Asymptotically cylindrical Ricci-flat manifolds

Author: Sema Salur
Journal: Proc. Amer. Math. Soc. 134 (2006), 3049-3056
MSC (2000): Primary 53C15, 53C21; Secondary 58J05
Published electronically: April 13, 2006
MathSciNet review: 2231631
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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

Keywords: Differential geometry, global analysis, analysis on manifolds
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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