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

BRASIL JR, ALDIR, COLARES, A. GERVASIO

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

AUTOR(ES)

BRASIL JR, ALDIR, COLARES, A. GERVASIO

FONTE

Anais da Academia Brasileira de Ciências

DATA DE PUBLICAÇÃO

2000-12

RESUMO

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 $\overline{R}$ = (R - 1) > 0 and $\overline{R}$ <= sup H² <= C $\scriptstyle \overline{R}$ , where C $\scriptstyle \overline{R}$ is a constant depending only on R and n. It is proved that either sup H² = $\overline{R}$ and Mn is totally umbilical, or sup H² = C $\scriptstyle \overline{R}$ and Mn is the hyperbolic cylinder H¹(1 - coth²r) x Sn - 1 (1 - tanh²r).

ACESSO AO TEXTO COMPLETO

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