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

Yaning Wang. "A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors." Open Mathematics 14.1 (2016): 977-985. <http://eudml.org/doc/287148>.

@article{YaningWang2016,
abstract = {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].},
author = {Yaning Wang},
journal = {Open Mathematics},
keywords = {Almost Kenmotsu manifold; Harmonic curvature tensor; Lie group; (k, μ, ν)-nullity condition; almost Kenmotsu manifold; harmonic curvature tensor; -nullity condition},
language = {eng},
number = {1},
pages = {977-985},
title = {A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors},
url = {http://eudml.org/doc/287148},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Yaning Wang
TI - A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 977
EP - 985
AB - 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].
LA - eng
KW - Almost Kenmotsu manifold; Harmonic curvature tensor; Lie group; (k, μ, ν)-nullity condition; almost Kenmotsu manifold; harmonic curvature tensor; -nullity condition
UR - http://eudml.org/doc/287148
ER -