In this paper, we introduce k-Ricci curvature and k-scalar curvature on lightlike hypersurface of a Lorentzian manifold with semi-symmetric metric connection. Using this curvatures, we establish some inequalities for lightlike hypersurface of a Lorentzian manifold with semi-symmetric metric connection. Considering these inequalities, we obtain the relation between Ricci curvature and scalar curvature endowed with semi-symmetric metric connection.

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We introduce a new class of lightlike submanifolds, namely, Screen Transversal Cauchy Riemann (STCR)-lightlike submanifolds, of indefinite K?hler manifolds. We show that this new class is an umbrella of screen transversal lightlike, screen transversal totally real lightlike and CR-lightlike submanifolds. We give a few examples of a STCR lightlike submanifold, investigate the integrability of various distributions, obtain a characterization of such lightlike submanifolds in a complex space form and find new conditions for the induced connection to be a metric connection. Moreover, we investigate the existence of totally umbilical (STCR)-lightlike submanifolds and minimal (STCR)-lightlike submanifolds. The paper also contains several examples.

In this paper, we study semi-invariant coisotropic lightlike submanifolds of a golden semi-Riemannian manifold. We give some necessary and sufficient conditions on integrability of distibutions on semi-invariant coisotropic lightlike submanifolds of a golden semi-Riemannian manifold. We obtain some geometric results for coisotropic lightlike submanifolds of a golden semi-Riemannian manifold. Moreover, we give an example.