New characterizations of spacelike hyperplanes in the steady state space

• Cícero P. Aquino ; Halyson I. Baltazar ^[1] ; Henrique F. de Lima ^[2]
  1. [1] Universidade Federal do Piauí

     Universidade Federal do Piauí

     Brasil

     
  2. [2] Universidade Federal de Campina Grande

     Universidade Federal de Campina Grande

     Brasil

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 126, Nº 1, 2020, págs. 61-72
• Idioma: inglés
• DOI: 10.7146/math.scand.a-117703
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space Sn+11 which is known as the steady state space Hn+1. Under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we are able to prove that they must be spacelike hyperplanes of Hn+1. Furthermore, through the analysis of the hyperbolic cylinders of Hn+1, we discuss the importance of the main hypothesis in our results. Our approach is based on a generalized maximum principle at infinity for complete Riemannian manifolds.