Author
Wenjie Wang
Bio: Wenjie Wang is an academic researcher. The author has contributed to research in topics: Ricci curvature. The author has an hindex of 1, co-authored 1 publications receiving 4 citations.
Topics: Ricci curvature
Papers
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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.
Abstract: In this paper, we prove that 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. c ©2016 All rights reserved.
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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.
Abstract: In this paper, we give a local characterization for the Ricci tensor of an almost Kenmotsu 3-manifold (M,ϕ,ξ,η,g) to be cyclic-parallel. As an application, we prove that if M has cyclic-parallel Ri...
3 citations
TL;DR: In this paper , the authors considered the notion of Cotton soliton on almost Kenmotsu 3-manifolds and proved a non-existence of such a soliton.
TL;DR: In this paper, a three-dimensional almost Kenmotsu manifold M3 satisfying the generalized (κ, μ)′-nullity condition is investigated, and the Ricci tensor of M3 is of Codazzi type.
Abstract: In this paper, a three-dimensional almost Kenmotsu manifold M3 satisfying the generalized (κ, μ)′-nullity condition is investigated. We mainly prove that on M3 the following statements are equivalent: (1) M3 is φ-symmetric; (2) the Ricci tensor of M3 is cyclic-parallel; (3) the Ricci tensor of M3 is of Codazzi type; (4) M3 is conformally flat with scalar curvature invariant along the Reeb vector field; (5) M3 is locally isometric to either the hyperbolic spaceH3(−1) or the Riemannian productH2(−4) ×R.
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TL;DR: In this article, the authors considered the notion of Cotton soliton within the framework of almost Kenmotsu 3-$h$-manifolds and proved a non-existence of such a soliton.
Abstract: In this paper, we consider the notion of Cotton soliton within the framework of almost Kenmotsu 3-$h$-manifolds First we consider that the potential vector field is pointwise collinear with the Reeb vector field and prove a non-existence of such Cotton soliton Next we assume that the potential vector field is orthogonal to the Reeb vector field It is proved that such a Cotton soliton on a non-Kenmotsu almost Kenmotsu 3-$h$-manifold such that the Reeb vector field is an eigen vector of the Ricci operator is steady and the manifold is locally isometric to $\mathbb{H}^2(-4) \times \mathbb{R}$