Riemann solitons on para-Sasakian geometry - De, K.; De, U.C. (Carpathian Mathematical Publications, 2022)
The goal of the present article is to investigate almost Riemann soliton and gradient almost Riemann soliton on 3-dimensional para-Sasakian manifolds. At first, it is proved that if (g, Z,λ) is an almost Riemann soliton on a para-Sasakian manifold M^3, then it reduces to a Riemann soliton and M^3 is of constant sectional curvature -1, provided the soliton vector Z has constant divergence. Besides these, we prove that if Z is pointwise collinear with the characteristic vector field ξ, then Z is a constant multiple of ξ and the manifold is of constant sectional curvature -1. Moreover, the almost Riemann soliton is expanding. Furthermore, it is established that if a para-Sasakian manifold M^3 admits gradient almost Riemann soliton, then M^3 is locally isometric to the hyperbolic space H^3(-1). Finally, we construct an example to justify some results of our paper.