Invariant submanifolds of generalized Sasakian-space-forms

TL;DR

This paper investigates invariant submanifolds within generalized Sasakian-space-forms, exploring conditions for total geodesicity and analyzing Ricci solitons, with new theoretical results and examples.

Contribution

It provides new necessary and sufficient conditions for invariant submanifolds to be totally geodesic and studies Ricci solitons in this geometric context.

Findings

Derived conditions for totally geodesic invariant submanifolds.

Presented examples of invariant submanifolds in generalized Sasakian-space-forms.

Analyzed Ricci solitons on these submanifolds.

Abstract

The present paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide some examples of such submanifolds and obtain many new results including, the necessary and sufficient conditions under which the submanifolds are totally geodesic. The Ricci solitons of such submanifolds are also studied.