Slant Lightlike Submanifolds of Semi-Riemannian Product Manifolds - Kumar, Tejinder; Kumar, Sangeet; Kumar, Pankaj (Sarajevo Journal of Mathematics, 2024)
The aim of the present paper is to investigate geometric characteristics of slant lightlike submanifolds of semi-Riemannian product manifolds. We obtain characterization theorems for the existence of slant lightlike submanifolds of semi-Riemannian product manifolds. We also find a necessary and sufficient condition enabling the induced connection on slant lightlike submanifolds of semi-Riemannian product manifolds to be a metric connection. Then, we establish some results for the integrability of distributions associated with this class of lightlike submanifolds. Consequently, we investigate totally umbilical slant lightlike submanifolds of semi-Riemannian product manifolds. In particular, we prove that every totally umbilical slant lightlike submanifold of a semi-Riemannian product manifold is always totally geodesic.