Yamabe solitons on 3-dimensional cosymplectic manifolds

Abstract

In this paper, it has been proved that if a 3-dimensional cosymplectic manifold M 3 admits a Yamabe soliton, then either M 3 is locally flat or the potential field is a contact vector field. Some special potential vector fields of Yamabe solitons on 3-dimensional cosymplectic manifolds have been considered and some other results have been obtained. Also, for general ð2n þ 1Þ-dimensional case, it will be shown that if an f À cosymplectic manifold M 2nþ1 admits a contact Yamabe soliton structure, then M 2nþ1 is a cosymplectic manifold. Finally, an example of Yamabe soliton on a 3-dimensional cosymplectic manifold is provided.