Screen transversal Cauchy-Riemann lightlike submanifolds of semi-Riemannian product manifolds

Abstract

We introduce screen transversal Cauchy-Riemann (STCR)-lightlike submanifolds of semi-Riemannian product manifolds. We obtain new conditions for the induced connection to be a metric connection. We investigate geometry of screen transversal Cauchy-Riemann (STCR)-lightlike submanifolds and investigate the integrability of various distributions of such lightlike submanifolds. Finally, we find conditions for minimal STCR-lightlike submanifolds of semi-Riemannian product manifolds. Moreover, we two give examples.