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THREE-DIMENSIONAL ALMOST KENMOTSU MANIFOLDS WITH η-PARALLEL RICCI TENSOR

Yaning Wang
대한수학회 (The Korean Mathematical Society)|2017.05|대한수학회지 (Journal of the KMS)|제54권 제3호|pp. 793-805

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참고문헌

키워드

$3$-dimensional almost Kenmotsu manifold$\eta$-parallel parallel Ricci tensornon-unimodular Lie group
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초록

In this paper, we prove that the Ricci tensor of a three-dimensional almost Kenmotsu manifold satisfying $\nabla_\xi h=0$, $h\neq0$, is $\eta$-parallel if and only if the manifold is locally isometric to either the Riemannian product $\mathbb{H}^{2}(-4)\times\mathbb{R}$ or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure.

Abstract

In this paper, we prove that the Ricci tensor of a three-dimensional almost Kenmotsu manifold satisfying $\nabla_\xi h=0$, $h\neq0$, is $\eta$-parallel if and only if the manifold is locally isometric to either the Riemannian product $\mathbb{H}^{2}(-4)\times\mathbb{R}$ or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure.

참고문헌 (18)

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