호남수학학술지 (Honam Mathematical Journal)

  • 제39권4호
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  • Pages.465-473
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  • 2017
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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ON A TOTALLY UMBILIC HYPERSURFACE OF FIRST ORDER

  • Kim, Jaeman (Department of Mathematics Education, Kangwon National University)
  • 투고 : 2016.09.06
  • 심사 : 2017.09.04
  • 발행 : 2017.12.25
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초록

In this paper, we define a totally umbilic hypersurface of first order and show that a totally umbilic hypersurface of first order in an Einstein manifold has a parallel second fundamental form. Furthermore we prove that a complete, simply connected and totally umbilic hypersurface of first order in a space of constant curvature is a Riemannian product of Einstein manifolds. Finally we show a proper example which is a totally umbilic hypersurface of first order but not a totally umbilic hypersurface.

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참고문헌

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