Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THREE-DIMENSIONAL ALMOST KENMOTSU MANIFOLDS WITH η-PARALLEL RICCI TENSOR

  • Wang, Yaning (Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control School of Mathematics and Information Sciences Henan Normal University)
  • Received : 2016.04.14
  • Published : 2017.05.01
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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.

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References

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