Pseudo-totally umbilical lightlike submanifolds

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, that leaves $M^{*}$, distribution over $M$, non-degenerate submanifolds $\bar{M}$, either contained in semi-Euclidean spheres or hyperbolic spaces. Moreover, tangible examples constructed this case. Finally, notion mean sectional curvatures relate them well-known tensors used characterisation space-times.