Study on para-Sasakian manifolds admitting η-Einstein soliton

Abstract

In this paper we explore the properties of para-Sasakian manifold with the help of Schouten-van Kampen connection. We examine para-Sasakian manifold admitting $\eta $-Einstein soliton with respect to this connection. Moreover, we investigate $\eta $-Einstein soliton on para-Sasakian manifolds admitting cyclic parallel Ricci tensor with respect to Schouten-van Kampen connection. Additionally, we investigate $\eta $-Einstein soliton on para-Sasakian manifolds satisfying $\overline{K} (\xi ,\digamma _{1}).\overline{S}=0$, $\overline{K}(\xi ,\digamma _{1}).\overline{R}=0$, for all smooth vector fields $\digamma _{1}$, where $\overline{K}$, $\overline{S}$ \ and $\overline{R}$ are conharmonic curvature tensor, Ricci curvature tensor and Riemannian curvature tensor with respect to Schouten-van Kampen connection, respectively.