Asymptotically Cylindrical Ricci-Flat Manifolds
Differential Geometry
2007-05-23 v2 Geometric Topology
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.
Cite
@article{arxiv.math/0410063,
title = {Asymptotically Cylindrical Ricci-Flat Manifolds},
author = {Sema Salur},
journal= {arXiv preprint arXiv:math/0410063},
year = {2007}
}
Comments
This version will appear in Proc. Amer. Math. Soc