Pointwise bi-slant lightlike submanifolds of indefinite nearly Kähler manifolds

Abstract

In this paper, we introduce the notion of pointwise bi-slant lightlike submanifolds of an indefinite nearly Kähler manifold and provide a characterization theorem for the existence of these submanifolds. Following this, we provide a non-trivial example of pointwise bi-slant lightlike submanifolds of indefinite nearly Kähler manifolds and then derive some conditions for the distributions associated with this class of submanifolds to be involutive. Further, we provide a characterization for a pointwise bi-slant lightlike submanifold of an indefinite nearly Kähler manifold to be a bi-slant lightlike submanifold and investigate the geometry of totally umbilical pointwise bi-slant lightlike submanifold of an indefinite nearly Kähler manifold. Finally, we obtain necessary and sufficient conditions for foliations determined by distributions on pointwise bi-slant lightlike submanifolds of an indefinite nearly Kähler manifold to be totally geodesic.