Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection

Abstract

We study lightlike submanifolds of a semi-Riemannian product manifold. We introduce a class of lightlike submanifolds called screen semi-invariant lightlike submanifold. We consider lightlike submanifolds with respect to a quarter symmetric non-metric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.