대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제56권1호
  • /
  • Pages.253-263
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  • 2019
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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CURVATURE HOMOGENEITY AND BALL-HOMOGENEITY ON ALMOST COKӒHLER 3-MANIFOLDS

  • Wang, Yaning (School of Mathematics and Information Sciences Henan Normal University)
  • 투고 : 2018.03.13
  • 심사 : 2018.06.21
  • 발행 : 2019.01.31
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초록

Let M be a curvature homogeneous or ball-homogeneous non-$coK{\ddot{a}}hler$ almost $coK{\ddot{a}}hler$ 3-manifold. In this paper, we prove that M is locally isometric to a unimodular Lie group if and only if the Reeb vector field ${\xi}$ is an eigenvector field of the Ricci operator. To extend this result, we prove that M is homogeneous if and only if it satisfies ${\nabla}_{\xi}h=2f{\phi}h$, $f{\in}{\mathbb{R}}$.

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참고문헌

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