Glasgow Mathematical Journal

Research Article

UNIQUENESS OF COMPLETE HYPERSURFACES WITH BOUNDED HIGHER ORDER MEAN CURVATURES IN SEMI-RIEMANNIAN WARPED PRODUCTS

C. P. AQUINOa1a2 and H. F. DE LIMAa3

a1 Departamento de Matemática, Universidade Federal do Piauí, Teresina, Piauí, 64049-550, Brazil

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

a3 Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande, Paraíba, 58109-970, Brazil e-mail: henrique.delima@pq.cnpq.br

Abstract

In this paper, we deal with complete hypersurfaces immersed with bounded higher order mean curvatures in steady state-type spacetimes and in hyperbolic-type spaces. By applying a generalised maximum principle for the Yau's square operator [11], we obtain uniqueness results in each of these ambient spaces.

(Received December 16 2010)

(Accepted June 11 2011)

2000 Mathematics Subject Classification

  • Primary 53C42;
  • Secondary 53B30;
  • 53C50;
  • 53Z05;
  • 83C99