Screen Transversal Cauchy Riemann Lightlike Submanifolds

Abstract

We introduce a new class of lightlike submanifolds, namely, Screen Transversal Cauchy Riemann (STCR)-lightlike submanifolds, of indefinite K\"{a}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.