Certain solitons on $\alpha$-cosymplectic manifolds

Abstract

In the present paper, we characterize some solitons such as $\eta$-Einstein soliton, $\eta$-Yamabe soliton and Ricci-Yamabe soliton on $\alpha$-cosymplectic manifolds. Furthermore, we characterize $3$-dimensional $\alpha$-cosymplectic manifolds with gradient Ricci-Yamabe soliton. Finally, we construct an example.