A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors
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In this paper, the curvature tensor of a 3D almost Kenmotsu manifold is shown to be harmonic if and only if the manifold is locally isometric to either the hyperbolic space or the Riemannian product ℍ2(−4) × ℝ.Abstract:
Abstract Let M3 be a three-dimensional almost Kenmotsu manifold satisfying ▽ξh = 0. In this paper, we prove that the curvature tensor of M3 is harmonic if and only if M3 is locally isometric to either the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(−4) × ℝ. This generalizes a recent result obtained by [Wang Y., Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math., 2016, 116, 79-86] and [Cho J.T., Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J., 2016, 45, 435-442].read more
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Ricci solitons on almost Kenmotsu 3-manifolds
TL;DR: In this article, it was shown 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 Kenmotsusu structure.
Journal ArticleDOI
Conformally Flat Almost Kenmotsu 3-Manifolds
TL;DR: In this paper, a necessary and sufficient condition for an almost Kenmotsu 3-manifold to be conformally flat is given. But this condition is not applicable to the case of the Riemannian product.
Journal ArticleDOI
Almost Kenmotsu 3−h -manifolds with cyclic-parallel Ricci tensor
TL;DR: The Ricci tensor of an almost Kenmotsu 3-h manifold is cyclic-parallel if and only if it is parallel and hence, the manifold is locally isometric to either the hyperbolic space H3(−1) or the Riemannian product H2(−4)× R as mentioned in this paper.
Journal ArticleDOI
Cyclic-parallel Ricci tensors on a class of almost Kenmotsu 3-manifolds
Yaning Wang,Xinxin Dai +1 more
TL;DR: In this article, the Ricci tensor of an almost Kenmotsu 3-manifold (M,ϕ,ξ,η,g) was shown to be cyclic-parallel.
References
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Almost contact structures and curvature tensors
Dirk Janssens,Lieven Vanhecke +1 more
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Almost Kenmotsu manifolds and local symmetry
Giulia Dileo,Anna Maria Pastore +1 more
TL;DR: In this paper, the authors consider locally symmetric almost Kenmotsu manifold and show that the manifold is locally isometric to the Riemannian product of an n+1-dimensional manifold of constant curvature.
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