$\mathcal{Z}$-symmetries of $(\epsilon)$-para-Sasakian 3-manifolds

TL;DR

This paper investigates specific curvature conditions related to the $ abla$ tensor on $(b5)$-para-Sasakian 3-manifolds, providing characterizations of various $ abla$-symmetry conditions.

Contribution

It characterizes $ abla$-symmetry, $ abla$-semisymmetry, $ abla$-pseudosymmetry, and projectively $ abla$-semisymmetry conditions on $(b5)$-para-Sasakian 3-manifolds.

Findings

Characterization of $ abla$-symmetric $(b5)$-para-Sasakian 3-manifolds.

Conditions for $ abla$-semisymmetry and $ abla$-pseudosymmetry.

Criteria for projectively $ abla$-semisymmetry.

Abstract

The object of this paper is study $(\epsilon)$-para-Sasakian 3-manifolds satisfying certain conditions on the $\mathcal{Z}$ tensor. We characterize, $\mathcal{Z}$-symmetric; $\mathcal{Z}$-semisymmetric; $\mathcal{Z}$-pseudosymmetric; and projectively $\mathcal{Z}$-semisymmetric conditions on an $(\epsilon)$-para-Sasakian 3-manifold.