# Ricci solitons on almost Kenmotsu 3-manifolds

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1236-1243
- ISSN: 2391-5455

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topYaning 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 -

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