Beta-almost Ricci solitons on almost CoKahler manifolds
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In the present paper is to classify Beta-almost ($\beta$-almost) Ricci solitons and $\beta$-almost gradient Ricci solitons on almost CoK\"ahler manifolds with $\xi$ belongs to $(k,\mu)$-nullity distribution. In this paper, we prove that such manifolds with $V$ is contact vector field and $Q\phi = \phi Q$ is $\eta$-Einstein and it is steady when the potential vector field is pointwise collinear to the reeb vectoer field. Moreover, we prove that a $(k,\mu)$-almost CoK\"ahler manifolds admitting $\beta$-almost gradient Ricci solitons is isometric to a sphere.
Abstract
In the present paper is to classify Beta-almost ($\beta$-almost) Ricci solitons and $\beta$-almost gradient Ricci solitons on almost CoK\"ahler manifolds with $\xi$ belongs to $(k,\mu)$-nullity distribution. In this paper, we prove that such manifolds with $V$ is contact vector field and $Q\phi = \phi Q$ is $\eta$-Einstein and it is steady when the potential vector field is pointwise collinear to the reeb vectoer field. Moreover, we prove that a $(k,\mu)$-almost CoK\"ahler manifolds admitting $\beta$-almost gradient Ricci solitons is isometric to a sphere.
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