Publications de l'Institut Mathématique, Nouvelle Série Vol. 98(112), pp. 227–235 (2015) 

Gradient Ricci solitons on almost Kenmotsu manifoldsYaning Wang, Uday Chand De, Ximin LiuCollege of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, China; Department of Pure Mathematics, University of Calcutta, Kolkata, India; School of Mathematical Sciences, Dalian University of Technology, Dalian, ChinaAbstract: 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 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.
© 2015 Mathematical Institute of the Serbian Academy of Science and Arts
