Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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
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Abstract

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 $\bar{g}$.

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References

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  2. Tsukuba J. Math. v.3 On codimension one isometric immersions between indefinite space forms Graves, L.
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  4. Semi-Riemannian Geometry with Applications to Relativity O'Neil, B.
  5. Introduction to Differential Geometry v.Ⅳ Spivak, M.