The geometric characteristics of SGL submanifolds in an indefinite Sasakian statistical manifold equipped with a quarter symmetric metric connection

TL;DR

This paper investigates the geometric properties of SGL submanifolds within indefinite Sasakian statistical manifolds equipped with a quarter-symmetric metric connection, focusing on integrability, parallelism, and geodesic conditions.

Contribution

It provides new theoretical insights into the structure and behavior of SGL submanifolds in this specific geometric setting, including conditions for integrability and geodesicity.

Findings

Analysis of integrability conditions for distributions

Conditions for parallelism of distributions

Existence of totally geodesic foliations and examples

Abstract

This research paper examines the geometric structure of screen generic lightlike (SGL) submanifolds in an indefinite Sasakian statistical manifold equipped with a quarter-symmetric (QS) metric connection. The study focuses on analyzing the integrability conditions and the parallelism properties of various distributions associated with these submanifolds. It explores the characteristics of totally geodesic foliations and mixed geodesic submanifolds, providing significant insights into their geometric behavior. In addition to the theoretical development, the paper also presents an illustrative example of a contact SGL submanifold within an indefinite Sasakian statistical manifold.