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Almost Kenmotsu 3-\(h\)-manifolds with cyclic-parallel Ricci tensor. (English) Zbl 1345.53034

Summary: In this paper, we prove that the Ricci tensor of an almost Kenmotsu 3-\(h\)-manifold is cyclic-parallel if and only if it is parallel and hence, the manifold is locally isometric to either the hyperbolic space \(\mathbb H^3(-1)\) or the Riemannian product \(\mathbb H^2(-4)\times \mathbb R\).

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D15 Almost contact and almost symplectic manifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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