GCR-Lightlike Submanifolds of Indefinite Nearly Kaehler Manifolds

Abstract

Abstract. We introduce CR, SCR and GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds and obtain their existence in indefinite nearly Kaehler manifolds of constant holomorphic sectional curvature c and of constant type α. We also prove characterization theorems on the existence of totally umbilical and minimal GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds.

Integrability of the distributions of GCR-lightlike submanifolds of (ε)-Sasakian manifolds

“…Later on, Duggal and Bejancu [5] introduced the concept of CR-lightlike submanifolds of inde…nite Kaehler manifolds but which excluded the complex and totally real subcases, therefore Duggal and Sahin [6] introduced Screen Cauchy-Riemann (SCR)-lightlike submanifolds of in-de…nite Kaehler manifolds which included complex and screen real subcases but there was no inclusion relation between SCR and CR classes. Thus as an umbrella of complex, real hypersurfaces, screen real and CR-lightlike submanifolds, Duggal and Sahin [7] introduced Generalized Cauchy-Riemann (GCR)-lightlike submanifolds of inde…nite Kaehler manifolds and further studied by [10][11][12][13][14][15]. Since there are signi…cant applications of contact geometry in thermodynamics, optics, mechanics and many more.…”