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

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.