The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지

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

  • Published : 2009.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

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 $L^n$.

Keywords

References

  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.