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DOI QR Code

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

  • Wang, Yaning
  • Received : 2016.04.14
  • Published : 2017.05.01

Abstract

In this paper, we prove that the Ricci tensor of a three-dimensional almost Kenmotsu manifold satisfying ${\nabla}_{\xi}h=0$, $h{\neq}0$, 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.

Keywords

3-dimensional almost Kenmotsu manifold;${\eta}$-parallel parallel Ricci tensor;non-unimodular Lie group

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