Lightlike hypersurfaces of an indefinite Kaehler manifold of a quasi-constant curvature

We study lightlike hypersurfaces M of an indefinite Kaehler manifold M̅ of quasi-constant curvature subject to the condition that the characteristic vector field ζ of M̅ is tangent to M. First, we provide a new result for such a lightlike hypersurface. Next, we investigate such a lightlike hypersurface M of M̅ such that(1) the screen distribution S(TM) is totally umbilical or(2) M is screen conformal.

Lightlike hypersurfaces of metallic semi-Riemannian manifolds

In our paper, we introduce and study lightlike hypersurfaces of a metallic semi-Riemannian manifold. We examine some geometric properties of invariant lightlike hypersurfaces. We show that the induced structure on an invariant lightlike hypersurface is also metallic. We also define screen semi-invariant lightlike hypersurfaces, investigate integrability conditions for the distributions and give some examples.

Lightlike hypersurfaces of an (ε)-para Sasakian manifold with a semi-symmetric non-metric connection

In the present paper, we study a lightlike hypersurface, when the ambient manifold is an (?)-para Sasakian manifold endowed with a semi-symmetric non-metric connection. We obtain a condition for such a lightlike hypersurface to be totally geodesic. We define invariant and screen semi-invariant lightlike hypersurfaces of (?)-para Sasakian manifolds with a semi-symmetric non-metric connection. Also, we obtain integrability conditions for the distributions D ? ??? and D' ? ??? of a screen semi-invariant lightlike hypersurface of an (?)-para Sasakian manifolds with a semi-symmetric non-metric connection.

2-symmetric lightlike hypersurfaces in semi-Riemannian space forms

In this paper, we will investigate 2-symmetry type curvature conditions of a lightlike hypersurface of a semi-Riemannian space form. Then we find some results related with locally symmetric and 2-symmetric lightlike hypersurfaces. Finally the relation between semisymmetric and 2-symmetric lightlike hypersurfaces will be given.

Totally Umbilical Lightlike Hypersurfaces in Robertson-Walker Spacetimes

We study the problem of lightlike hypersurface immersed into Robertson-Walker (RW) spacetimes in this paper, where the screen bundle of the hypersurface has constant higher order mean curvature. We consider the following question: under what conditions is the compact lightlike hypersurface totally umbilical? Our approach is based on the relationship between the lightlike hypersurface with its screen bundle and the Minkowski formulae for the screen bundle.

On Lightlike Geometry of Para-Sasakian Manifolds

We study lightlike hypersurfaces of para-Sasakian manifolds tangent to the characteristic vector field. In particular, we define invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, respectively, and give examples. Integrability conditions for the distributions on a screen semi-invariant lightlike hypersurface of para-Sasakian manifolds are investigated. We obtain a para-Sasakian structure on the leaves of an integrable distribution of a screen semi-invariant lightlike hypersurface.