한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제16권4호
  • /
  • Pages.417-425
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  • 2009
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  • 1226-0657(pISSN)
  • /
  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
권호 표지

TOTALLY UMBILIC SPACELIKE SURFACES OF TYPE (I) IN $L^n$

  • 발행 : 2009.11.30
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초록

In this paper we show that spheres in $E^3{\subset}L^n$ and pseudohyperbolic spaces in $L^3{\subset}L^n$ are the only totally umbilic spacelike surfaces of type (I) in $L^n$.

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참고문헌

  1. Graves, L.: Codimension one isometric immersions betweem Lorentzian spaces. Trans. Amer. Math. Soc. 252 (1979), 367-392. https://doi.org/10.1090/S0002-9947-1979-0534127-4
  2. Graves, L.: On codimension one isometric immersions between indefinite space forms. Tsukuba J. Math. 3 (1979), no. 2, 17-29. https://doi.org/10.21099/tkbjm/1496158685
  3. Hoffman, D. & R. Osserman: The geometry of the generalized Gauss map. Memoires Amer. Math. Soc. 28, 1980.
  4. O'Neil, B.: Semi-Riemannian Geometry with application to Relativity. Academic Press, NY, 1983.
  5. Spivak, M.: Introduction to Differential Geometry IV, Publish or Perish Inc., Berkeley, CA, 1979.