Let (M3, g) be an almost Kenmotsu 3-manifold such that the Reeb vector field is an eigenvector field of the Ricci operator. In this paper, we prove that if g represents a Ricci soliton whose potential vector field is orthogonal to the Reeb vector field, then M3 is locally isometric to either the hyperbolic space ℍ3(−1) or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure. In particular, when g represents a gradient Ricci soliton whose potential vector field is orthogonal to the Reeb vector field, then M3 is locally isometric to either ℍ3(−1) or ℍ2(−4) × ℝ.
@article{bwmeta1.element.doi-10_1515_math-2017-0103,
author = {Yaning Wang},
title = {Ricci solitons on almost Kenmotsu 3-manifolds},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1236-1243},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0103}
}
Yaning Wang. Ricci solitons on almost Kenmotsu 3-manifolds. Open Mathematics, Tome 15 (2017) pp. 1236-1243. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0103/