On Ricci Recurrent Almost Kenmotsu $3$-manifolds

Year 2024, Volume: 17 Issue: 2, 538 - 550, 27.10.2024

Ji-eun Lee

https://doi.org/10.36890/iejg.1407888

Abstract

In this paper, we prove first that for an almost Kenmotsu $3$-manifold satisfying $\xi (tr \, h^2)=0$, its Ricci operator is recurrent if and only if the manifold is locally symmetric. Next, we show that $\varphi$-Ricci symmetry and $\varphi$-Ricci recurrence are equivalent conditions in almost Kenmotsu $3$-manifolds. Thus, an almost Kenmotsu $3$-manifold is $\varphi$-Ricci symmetric if and only if it has dominantly $\eta$-parallel Ricci operator.

Keywords

Almost Kenmotsu manifold, local symmetry, Ricci recurrent

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