SCREEN ISOTROPIC LEAVES ON LIGHTLIKE HYPERSURFACES OF A LORENTZIAN MANIFOLD

The curvatures of lightlike hypersurfaces of an indefinite Kenmotsu manifold

We study the forms of curvatures of lightlike hypersurfaces M of an indefinite Kenmotsu manifold M̄ subject to the conditions: (1) M is locally symmetric, i.e., the curvature tensor R of M be parallel on TM , or (2) M is a semi-symmetric manifold, i.e., R(X, Y )R = 0 on TM . M.S.C. 2010: 53C25, 53C40, 53C50.

Lightlike Hypersurfaces of a Trans-Sasakian Manifold with a Quarter-Symmetric Metric Connection

In this paper, we study the geometry of lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. The main result is a characterization theorem for such a lightlike hypersurface of an indefinite generalized Sasakian space form. Mathematics Subject Classification: 53C25, 53C40, 53C50

Lightlike Hypersurfaces of a Semi-Riemannian Product Manifold and Quarter-Symmetric Nonmetric Connections

We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical antiinvariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quartersymmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions ...

Indefinite trans-Sasakian manifold of quasi-constant curvature with lightlike hypersurfaces

In this paper, we study indefinite trans-Sasakian manifold M̄ of quasi-constant curvature with lightlike hypersurfaces M . We provide several new results on such a manifold M̄ , in which the characteristic 1form θ and the characteristic vector field ζ, defined by (1.1), are identical with the structure 1-form θ and the structure vector field ζ of the indefinite trans-Sasakian structure (J, ζ, θ) ...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form