Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton

Abstract

In this paper, we examine 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton. We give some theorems for $W_{0}^{*}$ flat, $\xi-W_{0}^{*}$ flat and $\phi-W_{0}^{*}$ semisymmetric 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton. Also we study conformal Ricci soliton on a 3-dimensional quasi-Sasakian manifold satisfying the conditions $W_{0}^{*}(\xi,X).S=0$ and $R(\xi,X).W_{0}^{*}=0$.