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Siberian Mathematical Journal

, Volume 37, Issue 3, pp 591–613 | Cite as

Conformal development of a curve in a Riemannian space into a Minkowski space

  • V. V. Slavskii
Article
  • 19 Downloads

Keywords

Minkowski Space Riemannian Space Conformal Development 
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References

  1. 1.
    é. Cartan, Spaces of Affine, Projective or Conformai Connection [Russian translation of a collection of articles], Kazansk. Univ., Kazan' (1962).Google Scholar
  2. 2.
    S. Kobayashi, Transformation Groups in Differential Geometry [Russian translation], Nauka, Moscow (1986).Google Scholar
  3. 3.
    Yu. G. Reshetnyak, Stability Theorems in Geometry and Analysis [in Russian], Nauka, Novosibirsk (1982).Google Scholar
  4. 4.
    I. G. Nikolaev and S. Z. Shefel', “Differential properties of mappings conformal at a point,” Sibirsk. Mat. Zh.,27, No. 1, 132–142 (1986).Google Scholar
  5. 5.
    V. V. Slavskii, “Conformally flat metrics and pseudo-Euclidean geometry,” Sibirsk. Mat. Zh.,35, No. 3, 674–682 (1994).Google Scholar
  6. 6.
    é. Cartan, Theory of Finite Continuous Groups and Differential Geometry Exposed by Means of the Moving Frame Method [Russian translation of two courses of lectures], Moscow Univ., Moscow (1963).Google Scholar
  7. 7.
    P. Griffiths, “On the Cartan method of Lie groups and moving frames as applied to existence and uniqueness questions in differential geometry,” Duke Math. J.,41, 775–814 (1974).CrossRefGoogle Scholar
  8. 8.
    é. Cartan, Geometry of Riemannian Spaces [Russian translation], ONTI, Moscow (1936).Google Scholar
  9. 9.
    A. L. Besse, Einstein Manifolds. Vol. 1 [Russian translation], Mir, Moscow (1990).Google Scholar
  10. 10.
    M. A. Akivis and V. V. Konnov, “Some local aspects of the theory of conformal structures,” Uspekhi Mat. Nauk,48, No. 1, 3–40 (1993).Google Scholar
  11. 11.
    H. Weyl, Gravitation und Elektrizitât, S.-B. Preuss. Akad. Wiss., Berlin, 1918, pp. 465–480.Google Scholar
  12. 12.
    G. B. Folland, “Weyl manifolds,” J. Differential Geom.,4, 145–153 (1970).Google Scholar
  13. 13.
    Yu. G. Reshetnyak, “On the concept of a lift of an irregular path in a fiber bundle and its applications,” Sibirsk. Mat. Zh.,16, No. 3, 588–598 (1975).Google Scholar
  14. 14.
    S. Sternberg, Lectures on Differential Geometry [Russian translation], Mir, Moscow (1970).Google Scholar
  15. 15.
    A. L. Besse, Einstein Manifolds. Vol. 2 [Russian translation], Mir, Moscow, pp. 315–703 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. V. Slavskii
    • 1
  1. 1.Barnaul

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