On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space

Anais da Academia Brasileira de Ciências

Aldir Brasil Jr¹  A. Gervasio Colares¹ 

[1] ,Universidade Federal do Ceará Departamento de Matemática Fortaleza CE ,Brazil

关键词: hyperbolic cylinder;    spacelike hypersurfaces;    de Sitter space;   

DOI  :  10.1590/S0001-37652000000400001

来源: SciELO

【 摘 要 】

Let Mn be a complete spacelike hypersurface with constant normalized scalar curvature R in the de Sitter Space S1n + 1. Let H the mean curvature and suppose that = (R - 1) > 0 and <= sup H² <= C, where C is a constant depending only on R and n. It is proved that either sup H² = and Mn is totally umbilical, or sup H² = C and Mn is the hyperbolic cylinder H¹(1 - coth²r) x Sn - 1 (1 - tanh²r).

【 授权许可】

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