General Relativity and Gravitation

, Volume 27, Issue 1, pp 71–84 | Cite as

Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes

  • Luis J. Alías
  • Alfonso Romero
  • Miguel Sánchez
Article

Abstract

A new technique is introduced in order to solve the following question:When is a complete spacelike hypersurface of constant mean curvature in a generalized Robertson-Walker spacetime totally umbilical and a slice? (Generalized Robertson-Walker spacetimes extend classical Robertson-Walker ones to include the cases in which the fiber has not constant sectional curvature.) First, we determine when this hypersurface must be compact. Then, all these compact hypersurfaces in (necessarily spatially closed) spacetimes are shown to be totally umbilical and, except in very exceptional cases, slices. This leads to proof of a new Bernstein-type result. The power of the introduced tools is also shown by reproving and extending several known results.

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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Luis J. Alías
    • 1
  • Alfonso Romero
    • 2
  • Miguel Sánchez
    • 2
  1. 1.Departamento de MatemàticasUniversidad de MurciaEspinardoSpain
  2. 2.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain

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