Open Mathematics (Jan 2016)

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

  • Wang Yaning

DOI
https://doi.org/10.1515/math-2016-0088
Journal volume & issue
Vol. 14, no. 1
pp. 977 – 985

Abstract

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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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