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

被引：0
作者：
Luis J. Alías
José A. Pastor
机构：
[1] Universidad de Murcia,Departamento de Matemáticas
来源：
Annals of Global Analysis and Geometry | 2000年 / 18卷
关键词：
hyperbolic image; Lorentz–Minkowski space; scalar curvature; spacelike hypersurfaces; volume;
D O I：
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学科分类号：
摘要：
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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页码：75 / 84
页数：9
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