대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제35권4호
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  • Pages.1221-1244
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  • 2020
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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LK-BIHARMONIC HYPERSURFACES IN SPACE FORMS WITH THREE DISTINCT PRINCIPAL CURVATURES

  • Aminian, Mehran (Department of Mathematics Vali-e-Asr University of Rafsanjan)
  • 투고 : 2020.02.15
  • 심사 : 2020.06.04
  • 발행 : 2020.10.31
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초록

In this paper we consider LK-conjecture introduced in [5, 6] for hypersurface Mn in space form Rn+1(c) with three principal curvatures. When c = 0, -1, we show that every L1-biharmonic hypersurface with three principal curvatures and H1 is constant, has H2 = 0 and at least one of the multiplicities of principal curvatures is one, where H1 and H2 are first and second mean curvature of M and we show that there is not L2-biharmonic hypersurface with three disjoint principal curvatures and, H1 and H2 is constant. For c = 1, by considering having three principal curvatures, we classify L1-biharmonic hypersurfaces with multiplicities greater than one, H1 is constant and H2 = 0, proper L1-biharmonic hypersurfaces which H1 is constant, and L2-biharmonic hypersurfaces which H1 and H2 is constant.

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참고문헌

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