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Hypersurfaces with constant k -th mean curvature in a Lorentzian space form

Shichang Shu — 2010

Archivum Mathematicum

In this paper, we study n ( n 3 ) -dimensional complete connected and oriented space-like hypersurfaces M n in an (n+1)-dimensional Lorentzian space form M 1 n + 1 ( c ) with non-zero constant k -th ( k < n ) mean curvature and two distinct principal curvatures λ and μ . We give some characterizations of Riemannian product H m ( c 1 ) × M n - m ( c 2 ) and show that the Riemannian product H m ( c 1 ) × M n - m ( c 2 ) is the only complete connected and oriented space-like hypersurface in M 1 n + 1 ( c ) with constant k -th mean curvature and two distinct principal curvatures, if the multiplicities of...

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