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].
@article{bwmeta1.element.doi-10_1515_math-2016-0088,
author = {Yaning Wang},
title = {A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {977-985},
zbl = {1355.53025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0088}
}
Yaning Wang. A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors. Open Mathematics, Tome 14 (2016) pp. 977-985. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0088/