Geodesic
Gradient Ricci Solitons on Almost Kenmotsu Manifolds
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 227

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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 $\lambda=4n$.
DOI : 10.2298/PIM140527001W
Classification : 53C25 53D15
Keywords: almost Kenmotsu manifold, gradient Ricci soliton, $\eta$-Einstein condition, nullity distribution 
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     author = {Yaning Wang and Uday C and and De and Ximin Liu},
     title = {Gradient {Ricci} {Solitons} on {Almost} {Kenmotsu} {Manifolds}},
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Yaning Wang; Uday C; and De; Ximin Liu. Gradient Ricci Solitons on Almost Kenmotsu Manifolds. Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 227 . doi: 10.2298/PIM140527001W

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