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 | References | Similar Articles | Additional Information

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 with Ricci-flat metric 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 and 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

DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08313-4

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.