Constant mean curvature hypersurfaces with constant angle in semi-Riemannian space forms

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

hypersurfaces with constant mean curvature in a lorentzian space form

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...

Stable constant mean curvature hypersurfaces in some Riemannian manifolds

We determine all stable constant mean curvature hypersurfaces in a wide class of complete Riemannian manifolds having a foliation whose leaves are umbilical hypersurfaces. Among the consequences of this analysis we obtain all the stable constant mean curvature hypersurfaces in many nonsimply connected hyperbolic space forms. Mathematics Subject Classification (1991). Primary 53A10; Secondary 49...

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...