Screen Transversal Cauchy Riemann Lightlike Submanifolds of Indefinite Kaehler Manifolds

TL;DR

This paper introduces a new class of lightlike submanifolds called Screen Transversal Cauchy Riemann (STCR)-lightlike submanifolds in indefinite Kaehler manifolds, exploring their properties, examples, and geometric conditions.

Contribution

It defines the STCR-lightlike submanifolds, unifies various existing classes, and investigates their integrability, existence of special subtypes, and geometric properties in indefinite Kaehler manifolds.

Findings

Characterization of STCR-lightlike submanifolds in complex space forms

Conditions for the induced connection to be metric

Existence of totally umbilical and minimal STCR-lightlike submanifolds

Abstract

We introduce a new class of lightlike submanifolds, namely, Screen Transversal Cauchy Riemann (STCR)-lightlike submanifolds, of indefinite Kaehler 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.