Abstract In this paper, it is proved that the Ricci operator of an almost Kenmotsu 3-h-manifold M is of transversely Killing-type if and only if M is locally isometric to the hyperbolic 3-space ℍ 3 ( − 1 ) {{\mathbb{H}}}^{3}(-1) or a non-unimodular Lie group endowed with a left invariant non-Kenmotsu almost Kenmotsu structure. This result extends those results obtained by Cho [Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J. 45 (2016), no. 3, 435–442] and Wang [Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math. 116 (2016), no. 1, 79–86; Three-dimensional almost Kenmotsu manifolds with η \eta -parallel Ricci tensor, J. Korean Math. Soc. 54 (2017), no. 3, 793–805].

中文翻译：

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具有横向杀死型 Ricci 算子的几乎 Kenmotsu 3-h-流形

摘要 本文证明了近Kenmotsu 3-h-流形M的Ricci算子是横向Killing型当且仅当M局部等距于双曲3-空间ℍ 3 ( − 1 ) {{ \mathbb{H}}}^{3}(-1) 或一个非单模李群赋有左不变的非Kenmotsu 几乎Kenmotsu 结构。这个结果扩展了 Cho [Local symmetry on几乎 Kenmotsu 三流形，北海道数学。J. 45 (2016)，没有。3, 435–442] 和 Wang [三维局部对称几乎 Kenmotsu 流形，安。波隆。数学。116 (2016)，没有。1, 79–86；三维几乎 Kenmotsu 流形与 η \eta -parallel Ricci 张量，J. Korean Math。社会。54 (2017), 没有。3, 793–805]。