A certain complete space-like hypersurface in Lorentz manifolds

Compact Space-like Hypersurfaces with Constant Scalar Curvature in Locally Symmetric Lorentz Spaces

Let Nn+p p be an (n + p)-dimensional connected semi-Riemannian manifold of index p. It is called a semi-definite space of index p. When we refer to index p, we mean that there are only p negative eigenvalues of semi-Riemannian metric of Nn+p p and the other eigenvalues are positive. In particular, Nn+1 1 is called a Lorentz space when p = 1. When the Lorentz space Nn+1 1 is of constant curvatur...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

A sharp height estimate for compact spacelike hypersurfaces with constant r-mean curvature in the Lorentz–Minkowski space and application

In this paper we obtain a sharp height estimate concerning compact spacelike hypersurfaces Σn immersed in the (n + 1)dimensional Lorentz–Minkowski space Ln+1 with some nonzero constant r-mean curvature, and whose boundary is contained into a spacelike hyperplane of Ln+1. Furthermore, we apply our estimate to describe the nature of the end of a complete spacelike hypersurface of Ln+1. © 2007 Els...

Kähler Metrics Generated by Functions of the Time-like Distance in the Flat Kähler-lorentz Space

We prove that every Kähler metric, whose potential is a function of the timelike distance in the flat Kähler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kähler manifolds with the above mentioned metrics. New examples of Sasakian space forms are obtained as real hypersurfaces of a Kähler space form ...