Asymptotically Cylindrical Ricci-Flat Manifolds

Details Asymptotically Cylindrical Ricci-Flat Manifolds Asymptotically Cylindrical Ricci-Flat Manifolds

2004-10-04

arxiv.org/abs/math/0410063v2

Proc. Amer. Math. Soc., 134 (2006), no. 10, 3049-3056.

Mathematics

Differential Geometry

This version will appear in Proc. Amer. Math. Soc

Scientific paper

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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