Integral formulae for spacelikehypersurfaces in conformally stationary spacetimes and applications

• Main Author: Alías, Luís J.
• Publication Date: 2003
• Other Authors: Brasil Júnior, Aldir Chaves, Colares, Antônio Gervásio
• Format: Article
• Language: eng
• Source: Repositório Institucional da Universidade Federal do Ceará (UFC)
• dARK ID: ark:/83112/0013000028b72
• Download full: http://www.repositorio.ufc.br/handle/riufc/4631
• topic: Hipersuperfícies; Campos vetoriais; Curvatura

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.