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A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors

100%

Wang Y.

Open Mathematics

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2016

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tom 14

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nr 1

977-985

EN

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].

2

Three-dimensional locally symmetric almost Kenmotsu manifolds

100%

Wang Y.

Annales Polonici Mathematici

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2016

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tom 116

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nr 1

79-86

EN

We prove that a three-dimensional almost Kenmotsu manifold is locally symmetric if and only if it is locally isometric to either the hyperbolic space ℍ³(-1) or the Riemannian product ℍ²(-4)×ℝ.

3

Ricci solitons on almost Kenmotsu 3-manifolds

100%

Wang Y.

Open Mathematics

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2017

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tom 15

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nr 1

1236-1243

EN

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.

4

Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions

63%

Wang Y., Liu X.

Annales Polonici Mathematici

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2014

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tom 112

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nr 1

37-46

EN

We consider an almost Kenmotsu manifold $M^{2n+1}$ with the characteristic vector field ξ belonging to the (k,μ)'-nullity distribution and h' ≠ 0 and we prove that $M^{2n+1}$ is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, provided that $M^{2n+1}$ is ξ-Riemannian-semisymmetric. Moreover, if $M^{2n+1}$ is a ξ-Riemannian-semisymmetric almost Kenmotsu manifold such that ξ belongs to the (k,μ)-nullity distribution, we prove that $M^{2n+1}$ is of constant sectional curvature -1.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Open Mathematics

4 Wang Y.

1 Liu X.

1 2017

2 2016

1 2014

A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors

Three-dimensional locally symmetric almost Kenmotsu manifolds

Ricci solitons on almost Kenmotsu 3-manifolds

Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions