대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제39권4호
  • /
  • Pages.681-685
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  • 2002
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON A CHARACTERIZATION OF ROUND SPHERES

  • Onat, Leyla (Department of Mathematics, Mersin University)
  • 발행 : 2002.11.01
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초록

It is shown that, an immersion of n-dimensional compact manifold without boundary into (n + 1)-dimensional Euclidean space, hyperbolic space or the open half spheres, is a totally umbilic immersion if for some r, r =2, 3, …, n the r-th mean curvature Hr does not vanish and there are nonnegative constants $C_1$, $C_2$, …, $C_{r}$ such that (equation omitted)d)

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참고문헌

  1. Proc. Amer. Math. Soc. v.88 no.1 Integral fomula and fyperspheres in a simply connected space form I. Bivens https://doi.org/10.2307/2045121
  2. J. Differential Geometry v.5 Some integral formulas for submanifolds and their applications B. Y. Chen;K. Yano
  3. Proc. Amer. Math. Soc. v.126 no.12 A Characterization of round spheres S. E. Koh https://doi.org/10.1090/S0002-9939-98-04589-4
  4. Bull. Korean Math. Soc. v.36 no.4 Another characterization of round spheres S. W. Lee;S. E. Koh
  5. Glasgow Math. J. v.43 Addendum to the paper: Sphere theorem by means of the ratio of mean curvature functions S. E. Koh;S- W Lee
  6. De Gruyter Berlin Global affine differential geometry of hypersurfaces A. M. Li;U. Simon;G. Zhao
  7. Affine Differential Geometry K. Nomizu;T. Sasaki

피인용 문헌

  1. A characterization of totally umbilical hypersurfaces in de Sitter space vol.51, pp.1, 2004, https://doi.org/10.1016/j.geomphys.2003.09.006