Invariant and anti-invariant submanifolds of special quasi-sasakian manifolds

TL;DR

This paper investigates the properties of invariant and anti-invariant submanifolds within special quasi-Sasakian manifolds, focusing on pseudo-parallelism and Ricci solitons, and establishes equivalences under certain conditions.

Contribution

It introduces new results on the equivalence of Chaki-pseudo and Deszcz-pseudo parallelism for these submanifolds and explores Ricci soliton metrics in this context.

Findings

Chaki-pseudo parallel and Deszcz-pseudo parallel classes are equivalent under specific conditions.

Invariant and anti-invariant submanifolds with Ricci soliton metrics are characterized.

Results hold for both Levi-Civita and semisymmetric metric connections.

Abstract

The present paper deals with the study of Chaki-pseudo parallel and Deszcz-pseudo parallel invariant submanifolds of SQ-Sasakian manifolds with respect to Levi-Civita connection and semisymmetric metric connection and obtain that these two classes are equivalent with a certain condition. Also the invariant and anti-invariant submanifolds of SQ-Sasakian manifolds with respect to Levi-Civita connection as well as semisymmetric metric connection whose metrics are Ricci solitons are studied.