Nearly Sasakian manifolds revisited

We provide a new, self-contained and more conceptual proof of the result that an almost contact metric manifold of dimension greater than 5 is Sasakian if and only if it is nearly Sasakian.

A note on quasi-generalized CR-lightlike geometry in indefinite nearly μ-Sasakian manifolds

The concept of quasi-generalized CR-lightlike was first introduced by the authors in [Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds, Arab. J. Math. 5 (2016) 87–101]. In this paper, we focus on ascreen and co-screen quasi-generalized CR-lightlike submanifolds of indefinite nearly [Formula: see text]-Sasakian manifold. We prove an existence theorem for minimal ascreen quasi-generalized CR-lightlike submanifolds admitting a metric connection. Classification theorems on nearly parallel and auto-parallel distributions on a co-screen quasi-generalized CR-lightlike submanifold are also given. Several examples are also constructed, where necessary, to illustrate the main ideas.