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- W3215364175 abstract "In this article we study a three dimensional contact metric manifold $M^3$ with Cotton solitons. We mainly consider two classes of contact metric manifolds admitting Cotton solitons. Firstly, we study a contact metric manifold with $Qxi = rhoxi$, where $rho$ is a smooth function on $M$ constant along Reeb vector field $xi$ and prove that it is Sasakian or has constant sectional curvature 0 or 1 if the potential vector field of Cotton soliton is collinear with $xi$ or is a gradient vector field. Moreover, if $rho$ is constant we prove that such a contact metric manifold is Sasakian, flat or locally isometric to one of the following Lie groups: $SU(2)$ or $SO(3)$ if it admits a Cotton soliton with the potential vector field being orthogonal to Reeb vector field $xi$. Secondly, it is proved that a $(kappa,mu,nu)$-contact metric manifold admitting a Cotton soliton with the potential vector field being Reeb vector field is Sasakian. Furthermore, if the potential vector field is a gradient vector field, we prove that $M$ is Sasakian, flat, a contact metric $(0,−4)$-space or a contact metric $(kappa,0)$-space with $kappa lt 1$ and $kappaneq0$. For the potential vector field being orthogonal to $xi$, if $nu$ is constant we prove that $M$ is either Sasakian, or a $(kappa,mu)$-contact metric space." @default.
- W3215364175 created "2021-12-06" @default.
- W3215364175 creator A5046561927 @default.
- W3215364175 date "2021-11-01" @default.
- W3215364175 modified "2023-10-12" @default.
- W3215364175 title "Three dimensional contact metric manifolds with Cotton solitons" @default.
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- W3215364175 doi "https://doi.org/10.32917/h2020064" @default.
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