Copyright q 2011 Rakesh Kumar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We study mixed geodesic GCR-lightlike submanifolds of indefinite Sasakian manifolds and obtain some necessary and sufficient conditions for a GCR...

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.

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,...

In this paper, we study the geometry of a semi-Riemannian manifold M̄ of quasi-constant curvature. The main result is two characterization theorems for M̄ endowed with a statical, screen homothetic or screen totally umbilical half lightlike submanifold M . Mathematics Subject Classification: 53C25, 53C40, 53C50

In this study, we introduce indefinite sasakian statistical manifolds and lightlike hypersurfaces of an manifold. Some relations among induced geometrical objects with respect to dual connections in a hypersurface manifold are obtained. examples related these concepts also presented. Finally, prove that invariant submanifold is