The purpose of the article is to characterize \textbf{gradient $(m,\rho)$-quasi Einstein solitons} within the framework of two classes of almost Kenmotsu Manifolds. Finally, we consider an example to justify a result of our paper. 

A note on gradient solitons on two classes of almost Kenmotsu manifolds

The purpose of the article is to characterize \textbf{gradient $(m,\rho)$-quasi Einstein solitons} within the framework of two classes of almost Kenmotsu Manifolds. Finally, we consider an example to justify a result of our paper.

A note on gradient Solitons on two classes of almost Kenmotsu Manifolds

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].

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

In this paper, we give a local characterization for the Ricci tensor of an almost Kenmotsu 3-manifold (M,ϕ,ξ,η,g) to be cyclic-parallel. As an application, we prove that if M has cyclic-parallel Ri...

Xinxin Dai

Papers

Cyclic-parallel Ricci tensors on a class of almost Kenmotsu 3-manifolds