In this article we investigate the geometry of CR-lightlike submanifolds in an indefinite Kähler product manifold. In particular, we obtain the necessary and sufficient conditions for a CR-lightlike submanifold in an indefinite Kähler product manifold to be either CR-lightlike product, or D-geodesic, or D′-geodesic. We also study totally umbilical and curvature-invariant CR-lightlike submanifol...

In this paper, we study half lightlike submanifolds M of an indefinite generalized Sasakian space form M̄(f1, f2, f3), with an indefinite trans-Sasakian structure of type (α, β), subject to the condition that the structure vector field of M̄ is tangent to M . Our main result is a characterization theorem for such a half lightlike submanifold. Mathematics Subject Classification: 53C25, 53C40, 53C50

We establish the links between lightlike geometry and basics invariants of associated semi-Riemannian on r-lightlike submanifold constructed from a ambient. Then we some basic inequalities, involving scalar curvature shape operator coisotropic in manifold. Equality cases are also discussed.

We study GCR-lightlike submanifolds of semi-Riemannian product manifolds. give some equivalent conditions for the integrability various distributions manifolds and investigate geometry leaves distributions.

This study looks into the bislant submanifolds of almost product semi-Riemannian manifolds that are Riemannian, and lightlike. We also state theorems provide required conditions for constructing a slant submanifold from submanifold. Morever, we define semi-slant locally discuss integrability distributions invariants or slants constitute

We introduce the geometry of pseudo-totally umbilical lightlike submanifold $M$ a semi-Riemannian manifold $\bar{M}$. In line with above, we give complete classification $1$-lightlike submanifolds, such as hypersurfaces and half-lightlike submanifolds. Furthermore, screen distributions are also investigated, for any whose umbilical. Closely linked to above show, under some geometric conditions,...