Scalar Curvature Rigidity for Asymptotically Locally Hyperbolic Manifolds

被引：0

作者：

Lars Andersson

Mattias Dahl

机构：

[1] Royal Institute of Technology,Department of Mathematics

来源：

Annals of Global Analysis and Geometry | 1998年 / 16卷

关键词：

asymptotically hyperbolic manifold; conformally compactEinstein manifold; Killing connection; Killing spinor; mass; rigidity; scalar curvature;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The argument is based on a study of the Dirac operator defined with respect to the Killing connection. The existence of asymptotic Killing spinors is related to the spin structure on the end. The expression for the mass is calculated and proven to vanish for conformally compact Einstein manifolds with conformal boundary a spherical space form, giving rigidity. In the four dimensional case, the signature of the manifold is related to the spin structure on the end and explicit formulas for the relevant invariants are given.

引用

页码：1 / 27

页数：26