INTEGRAL FORMULAE FOR SPACELIKE HYPERSURFACES IN CONFORMALLY STATIONARY SPACETIMES AND APPLICATIONS

Luis J. Alías; Aldir Brasil; A. Gervasio Colares

doi:10.1017/S0013091502000500

Abstract

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In this paper we develop general Minkowski-type formulae for compact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds admitting a timelike conformal field. We apply them to the study of the umbilicity of compact spacelike hypersurfaces in terms of their $r$-mean curvatures. We derive several uniqueness results, for instance, compact spacelike hypersurfaces are umbilical if either some of their $r$-mean curvatures are linearly related or one of them is constant.

AMS 2000 Mathematics subject classification: Primary 53C42. Secondary 53B30; 53C50; 53Z05; 83C99

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INTEGRAL FORMULAE FOR SPACELIKE HYPERSURFACES IN CONFORMALLY STATIONARY SPACETIMES AND APPLICATIONS

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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INTEGRAL FORMULAE FOR SPACELIKE HYPERSURFACES IN CONFORMALLY STATIONARY SPACETIMES AND APPLICATIONS

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