MMN-4069

In this article, we study contact metric manifolds admitting almost quasi-Yamabe solitons $(g, V,m, \lambda)$. First we prove that there does not exist a nontrivial almost quasi-Yamabe soliton whose potential vector field $V$ is pointwise collinear with the Reeb vector field $\xi$ on a contact metric manifold. For $V$ being orthogonal to $\xi$, we consider the three dimensional cases. Next we consider a non-Sasakian contact metric $(\kappa,\mu)$-manifold admitting a nontrivial closed almost quasi-Yamabe soliton and give a classification. Finally, for a closed almost quasi-Yamabe soliton on $K$-contact manifolds, we prove that either the soliton is trivial or $r-\lambda=m$ if $r-\lambda$ is nonnegative and attains a maximum on $M$, where $r$ is the scalar curvature.

Vol. 24 (2023), No. 2, pp. 1033-1048

DOI: 10.18514/MMN.2023.4069

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