Gradient Ricci solitons on almost Kenmotsu manifolds

Yaning Wang, Uday Chand De, Ximin Liu

Abstract: If the metric of an almost Kenmotsu manifold with conformal Reeb foliation is a gradient Ricci soliton, then it is an Einstein metric and the Ricci soliton is expanding. Moreover, let $(M^{2n+1},\phi,\xi,\eta,g)$ be an almost Kenmotsu manifold with $\xi$ belonging to the $(k,\mu)'$-nullity distribution and $h\neq0$. If the metric $g$ of $M^{2n+1}$ is a gradient Ricci soliton, then $M^{2n+1}$ is locally isometric to the Riemannian product of an $(n+1)$-dimensional manifold of constant sectional curvature $-4$ and a flat $n$-dimensional manifold, also, the Ricci soliton is expanding with $\lambda=4n$.

Keywords: almost Kenmotsu manifold; gradient Ricci soliton; $\eta$-Einstein condition; nullity distribution

Classification (MSC2000): 53C25; 53D15

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