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Scalar Curvature Rigidity for Asymptotically Locally Hyperbolic Manifolds

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, S-100 44, Stockholm, Sweden

    Lars Andersson & Mattias Dahl

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  1. Lars Andersson
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  2. Mattias Dahl
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Andersson, L., Dahl, M. Scalar Curvature Rigidity for Asymptotically Locally Hyperbolic Manifolds. Annals of Global Analysis and Geometry 16, 1–27 (1998). https://doi.org/10.1023/A:1006547905892

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  • DOI: https://doi.org/10.1023/A:1006547905892

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