Almost Kenmotsu 3-h-manifolds with transversely Killing-type Ricci operators

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 ℍ3(−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].

Keywords

• almost kenmotsu 3-manifold
• transversely killing operator
• symmetry
• 53d15
• 53c25