Complete space-like hypersurfaces of a de Sitter space with constant mean curvature

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

‎Spacelike hypersurfaces with constant $S$ or $K$ in de Sitter‎ ‎space or anti-de Sitter space

‎Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎$S$ and $K$ be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of $M^n$‎. ‎If $S$ or‎ ‎$K$ is constant‎, ‎nonzero and $M^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...

hypersurfaces with constant mean curvature in a lorentzian space form

Spacelike hypersurfaces in de Sitter space with constant higher-order mean curvature

ing from (2.6), we obtain that ∫ M ( H1Hr −Hr+1 〈N ,a〉dV = 0. (3.1) We know from Newton inequality [2] that Hr−1Hr+1 ≤ H2 r , where the equality implies that k1 = ··· = kn. Hence Hr−1 ( H1Hr −Hr+1 ≥Hr ( H1Hr−1−Hr ) . (3.2) It derives from Lemma 2.1 that 0≤H1/r r ≤H1/r−1 r−1 ≤ ··· ≤H1/2 2 ≤H1. (3.3) Thus we conclude that Hr−1 ( H1Hr −Hr+1 ≥Hr ( H1Hr1 −Hr ≥ 0, (3.4) and if r ≥ 2, the equalities h...

‎spacelike hypersurfaces with constant $s$ or $k$ in de sitter‎ ‎space or anti-de sitter space

‎let $m^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de sitter space or an anti-de‎ ‎sitter space‎, ‎$s$ and $k$ be the squared norm of the second‎ ‎fundamental form and gauss-kronecker curvature of $m^n$‎. ‎if $s$ or‎ ‎$k$ is constant‎, ‎nonzero and $m^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...