Yamabe Solitons and t-Quasi Yamabe Gradient Solitons on Riemannian Manifolds Admitting Concurrent-Recurrent Vector Fields

We consider a Riemannian manifold (M,g) admitting a concurrent-recurrent vector field for which the metric g is a Yamabe soliton or a t-quasi Yamabe gradient soliton. We show that if the metric of a Riemannian three-manifold (M, g) admitting a concurrent-recurrent vector field is a Yamabe soliton, then M is of constant negative curvature -a(2). In this case, we see that the potential vector field is Killing. Next, we show that if the metric of a Riemannian manifold M admitting concurrent-recurrent vector field is a non-trivial r-quasi Yamabe gradient soliton with potential function f, then M has constant scalar curvature and is equal to -n(n - 1)a(2). Finally, an illustrative example is presented.