Invariant submanifolds of (LCS)n-Manifolds with respect to quarter symmetric metric connection

TL;DR

This paper investigates invariant submanifolds within (LCS)n-manifolds under quarter symmetric metric connections, revealing that their mean curvature remains consistent across different connections and providing conditions and examples for these structures.

Contribution

It introduces the study of invariant submanifolds in (LCS)n-manifolds with respect to quarter symmetric metric connections, including curvature properties and equivalence conditions.

Findings

Mean curvature with respect to quarter symmetric and Levi-Civita connections are equal.

Constructed example illustrating the theoretical results.

Derived equivalent conditions for invariant submanifolds.

Abstract

The object of the present paper is to study invariant submanifolds of (LCS)n-manifolds with respect to quarter symmetric metric connection. It is shown that the mean curvature of an invariant submanifold of (LCS)n-manifold with respect to quarter symmetric metric connection and Levi-Civita connection are equal. An example is constructed to illustrate the results of the paper. We also obtain some equivalent conditions of such notion.