Totally umbilic lorentzian surfaces embedded in $L^n$

  • Hong, Seong-Kowan (Department of Mathematics Education, Pusan National University, Pusan 609-735)
  • Published : 1997.02.01


Define $\bar{g}{\upsilon, \omega) = -\upsilon_1\omega_1 + \cdots + \upsilon_n\omega_n$ for $\upsilon, \omega in R^n$. $R^n$ together with this metric is called the Lorentzian n-space, denoted by $L^n$, and $R^n$ together with the Euclidean metric is called the Euclidean n-space, denoted by $E^n$. A Lorentzian surface in $L^n$ means an orientable connected 2-dimensional Lorentzian submanifold of $L^n$ equipped with the induced Lorentzian metrix g from $\bar{g}$.


  1. Trans. Amer. Math. Soc. v.252 Codimension one isometric immersions between Lorentzian spaces Graves, L.
  2. Tsukuba J. Math. v.3 On codimension one isometric immersions between indefinite space forms Graves, L.
  3. Memories of American Math. Soc. v.28 The geometry of the generalized Gauss map Hoffman, D.;R.Osserman
  4. Semi-Riemannian Geometry with Applications to Relativity O'Neil, B.
  5. Introduction to Differential Geometry v.Ⅳ Spivak, M.