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Spacelike Hypersurfaces with Constant Scalar Curvature in the Lorentz–Minkowski Space

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Abstract

We show that the only compact spacelike hypersurfaces in the Lorentz–Minkowski space Ln+1 having nonzero constant scalar curvature and spherical boundary are the hyperbolic caps (with negative constant scalar curvature). One key ingredient in our proof will be an integral formula for the n-dimensional volume enclosed by the boundary of a compact spacelike hypersurface, in the case where the boundary is contained in a hyperplane of Ln+1. As a direct application of that integral formula we also derive an interesting result for the volume of spacelike hypersurfaces.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain. e-mail

    Luis J. Alías & José A. Pastor

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  1. Luis J. Alías
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  2. José A. Pastor
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Alías, L.J., Pastor, J.A. Spacelike Hypersurfaces with Constant Scalar Curvature in the Lorentz–Minkowski Space. Annals of Global Analysis and Geometry 18, 75–84 (2000). https://doi.org/10.1023/A:1006660924994

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  • DOI: https://doi.org/10.1023/A:1006660924994

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