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

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Wang Y.

Open Mathematics

2016

tom 14

nr 1

977-985

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].

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1 Open Mathematics

1 Wang Y.

1 2016

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