• 호남수학학술지
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• 제39권4호
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• pp.465-473
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• 2017

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.