$β$-almost solitons on almost co-kähler manifolds

The object of the present paper is to study $β$-almost Yamabe solitons and $β$-almost Ricci solitons on almost co-Kähler manifolds. In this paper, we prove that if an almost co-Kähler manifold $M$ with the Reeb vector field $ξ$ admits a $β$-almost Yamabe solitons with the potential vector field $ξ$ or $bξ$, where $b$ is a smooth function then manifold is $K$-almost co-Kähler manifold or the soliton is trivial, respectively. Also, we show if a closed $(κ,μ)$-almost co-Kähler manifold with $n>1$ and $κ<0$ admits a $β$-almost Yamabe soliton then the soliton is trivial and expanding. Then we study an almost co-Kähler manifold admits a $β$-almost Yamabe soliton or $β$-almost Ricci soliton with $V$ as the potential vector field, $V$ is a special geometric vector field.

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