Screen Cauchy Riemann lightlike submersions

Abstract

We introduce the notion of screen Cauchy Riemann (SCR) lightlike submersions from an indefinite Kahler manifold onto a lightlike manifold. We prove that SCR-lightlike submersions include complex (invariant) and screen real (anti-invariant) lightlike submersions. We study some properties of proper SCR-lightlike submersions, their invariant and anti-invariant subcases. We also study the geometry of complex lightlike submersions and show that the radical distribution defines a totally geodesic foliation.