Ricci solitons on almost Kenmotsu 3-manifolds

Yaning Wang. "Ricci solitons on almost Kenmotsu 3-manifolds." Open Mathematics 15.1 (2017): 1236-1243. <http://eudml.org/doc/288552>.

@article{YaningWang2017,
abstract = {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.},
author = {Yaning Wang},
journal = {Open Mathematics},
keywords = {Almost Kenmotsu 3-manifold; Ricci soliton; Non-unimodular Lie group},
language = {eng},
number = {1},
pages = {1236-1243},
title = {Ricci solitons on almost Kenmotsu 3-manifolds},
url = {http://eudml.org/doc/288552},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Yaning Wang
TI - Ricci solitons on almost Kenmotsu 3-manifolds
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1236
EP - 1243
AB - 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.
LA - eng
KW - Almost Kenmotsu 3-manifold; Ricci soliton; Non-unimodular Lie group
UR - http://eudml.org/doc/288552
ER -