‎We prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite Sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎We also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite Sasakian space forms‎.

‎we prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎we also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite sasakian space forms‎.

In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite pa...

In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, D -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained. D

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 introduce the notion of screen pseudo-slant lightlike submanifolds of indefinite Kaehler manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D1, D2 and RadTM on screen pseudo-slant lightlike submanifolds of an indefinite Kaehler manifold have been obtained. Further, we obtain necessary and suff...

The notion of being totally umbilic is considered for non-degenerate and degenerate submanifolds of semi-Riemanian manifolds. After some remarks on the general case, timelike and lightlike totally umbilic submanifolds of Lorentzian manifolds are discussed, along with their physical interpretation in view of general relativity. In particular, the mathematical notion of totally umbilic submanifol...

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 introduce the notion of radical transversal screen Cauchy-Riemann (SCR)- lightlike submanifolds indefinite Sasakian manifolds giving characterization theorem with some nontrivial examples such submanifolds. Integrability conditions distributions D1, D2, D and D? on SCR-lightlike an manifold have been obtained. Further, obtain necessary sufficient for foliations determined by a...