Hypersurfaces with Constant Scalar Curvature

Linear Weingarten hypersurfaces in a unit sphere

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].  

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...

Stable space-like hypersurfaces with constant scalar curvature in generalized Roberston-Walker spacetimes

In this paper we study stable spacelike hyersurfaces with constant scalar curvature in generalized Roberston-Walker spacetime M n+1 = −I ×φ F. M.S.C. 2000: 53B30, 53C42, 53C50.

Hypersurfaces of Constant Curvature in Space Forms

In this paper we shall discuss hypersurfaces M of space forms of constant curvature; where curvature means one of the symmetric functions of curvature associated to the second fundamental form. The values of the constant will be chosen so that the linearized equation will be an elliptic equation onM . For example, for surfaces in 3 the two possible curvatures are the mean curvature H and the Ga...

Constant k-curvature hypersurfaces in Riemannian manifolds

In [8], Rugang Ye proved the existence of a family of constant mean curvature hypersurfaces in an m+ 1-dimensional Riemannian manifold (M, g), which concentrate at a point p0 (which is required to be a nondegenerate critical point of the scalar curvature), moreover he proved that this family constitute a foliation of a neighborhood of p0. In this paper we extend this result to the other curvatu...