A note on quasi generalized CR-lightlike geometry in indefinite nearly $\mu$-Sasakian manifold

TL;DR

This paper studies a special class of submanifolds called quasi generalized CR-lightlike in indefinite nearly μ-Sasakian manifolds, providing existence, classification results, and examples to deepen understanding of their geometric properties.

Contribution

It introduces new results on the existence and classification of quasi generalized CR-lightlike submanifolds in indefinite nearly μ-Sasakian manifolds, including minimal and parallel distribution conditions.

Findings

Existence of minimal ascreen quasi generalized CR-lightlike submanifolds with metric connection.

Classification of nearly parallel and auto-parallel distributions on co-screen submanifolds.

Construction of explicit examples illustrating the theoretical results.

Abstract

The concept of quasi generalized CR-lightlike was first introduced by the authors in [18]. In this paper, we focus on ascreen and co-screen quasi generalized CR-lightlike submanifolds of indefinite nearly $\mu$-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.