Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Complete spacelike hypersurfaces in a Robertson–Walker spacetime

ALMA L. ALBUJERa1, FERNANDA E. C. CAMARGOa2 and HENRIQUE F. DE LIMAa3

a1 Departamento de Matemáticas, Campus Universitario de Rabanales, Universidad de Córdoba, 14071 Córdoba, Spain. e-mail: alma.albujer@uco.es

a2 Departamento de Matemática, Universidade Federal do Ceará, 60455-760 Fortaleza, Ceará, Brazil. e-mail: feccamargo@yahoo.com.br

a3 Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, 58109-970 Campina Grande, Paraíba, Brazil. e-mail: henrique@dme.ufcg.edu.br

Abstract

In this paper, as a suitable application of the well-known generalized maximum principle of Omori–Yau, we obtain uniqueness results concerning to complete spacelike hypersurfaces with constant mean curvature immersed in a Robertson–Walker (RW) spacetime. As an application of such uniqueness results for the case of vertical graphs in a RW spacetime, we also get non-parametric rigidity results.

(Received August 04 2010)

(Revised May 05 2011)

(Online publication July 13 2011)