Study of Ricci and Riemann soliton structures on concircularly ϕ-recurrent Sasakian manifolds

The object of this paper is to study some properties of Ricci soliton structures on concircularly ?-recurrent Sasakian manifolds. Initially, it is proved that a concircularly ?-recurrent Sasakian mani-fold is an Einstein manifold and as a consequence of this, the Weyl conformal curvature tensor satisfies W (?, X)Y = 0. Further, the characterization of the vector field admitting Ricci and Riemann soliton have been studied. Additionally, the three-dimensional locally concircularly ?-recurrent Sasakian manifolds have been considered with an example and also it has been shown that such a manifold admitting almost Ricci soliton reduces to Ricci soliton.