Ricci solitons on almost Kenmotsu 3-manifolds
Keyword(s):
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.
2018 ◽
Vol 62
(4)
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pp. 912-922
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2010 ◽
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pp. 951-960
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2010 ◽
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pp. 47-53
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2012 ◽
Vol 10
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pp. 1220022
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2019 ◽
Vol 9
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pp. 715-726
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2021 ◽
Vol 13(62)
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pp. 581-594
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2021 ◽
pp. 2150179
2012 ◽
Vol 55
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pp. 123-130
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