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June 2020 Contact 3-manifolds and $*$-Ricci soliton
Yaning Wang
Kodai Math. J. 43(2): 256-267 (June 2020). DOI: 10.2996/kmj/1594313553

Abstract

Let $(M,\phi,\xi,\eta,g)$ be a three-dimensional Kenmotsu manifold. In this paper, we prove that the triple $(g,V,\lambda)$ on $M$ is a $*$-Ricci soliton if and only if $M$ is locally isometric to the hyperbolic 3-space $\mathbf{H}^3(-1)$ and $\lambda=0$. Moreover, if $g$ is a gradient $*$-Ricci soliton, then the potential vector field coincides with the Reeb vector field. We also show that the metric of a coKähler 3-manifold is a $*$-Ricci soliton if and only if it is a Ricci soliton.

Citation

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Yaning Wang. "Contact 3-manifolds and $*$-Ricci soliton." Kodai Math. J. 43 (2) 256 - 267, June 2020. https://doi.org/10.2996/kmj/1594313553

Information

Published: June 2020
First available in Project Euclid: 9 July 2020

zbMATH: 07227749
MathSciNet: MR4121362
Digital Object Identifier: 10.2996/kmj/1594313553

Rights: Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics

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Vol.43 • No. 2 • June 2020
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