Complete spacelike CMC hypersurfaces in a Lorentzian space form

• Autores: Biaogui Yang, Ximin Liu
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 78, Fasc. 3-4, 2011, págs. 513-525
• Idioma: inglés
• DOI: 10.5486/pmd.2011.4476
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• Resumen

  • Let x : Mn �¨ M n+1 1 (c) be a complete spacelike hypersurface immersed into a Lorentzian space form, where M n+1 1 (c) is a Lorentz{Minkowski space Ln+1 = Rn+1 1 , a de Sitter space Sn+1 1 �¼ Rn+2 1 or an anti-de Sitter space Hn+1 1 �¼ Rn+2 2 , according to c = 0, c = 1 or c = .1, respectively. Let . = .x, a. and �Õ = ..H , a., where .H is the mean curvature vector eld of Mn and a is a xed nonzero vector in the corre- sponding pseudo-Euclidean space. We prove that if Mn has constant mean curvature (CMC), and . = �É�Õ, for some real number �É, then Mn is a spacelike isoparametric hypersurface of M n+1 1 (c). Furthermore, it is either a totally umbilical hypersurface or a hyperbolic cylinder.