A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors
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AbstractLet 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].
2015 ◽
Vol 98
(112)
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pp. 227-235
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2015 ◽
Vol 22
(1)
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pp. 15-24
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2018 ◽
Vol 33
(2)
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pp. 255