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Russian Physics Journal

, Volume 35, Issue 10, pp 974–980 | Cite as

Conformally flat stäckel spaces and the problem of separation of variables in the Laplace-Beltrami equation

  • V. G. Bagrov
  • B. F. Samsonov
Elementary Particle Physics And Field Theory
  • 20 Downloads

Abstract

A full proof of the statement that all orthogonal systems of coordinates admitting separation of variables in the Laplace-Beltrami equation are cyclidal coordinates is presented

Keywords

Orthogonal System Full Proof 
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Literature cited

  1. 1.
    W. Miller, Symmetry and Separation of Variables [Russian translation], Mir, Moscow (1981).Google Scholar
  2. 2.
    E. G. Kalnins and W. Miller Jr., J. Math. Phys.,18, No. 1, 1–16 (1977); J. Math. Phys.,18, No. 2, pp. 271–280 (1977); J. Math. Phys.,19, No. 6, 1233–1246, 1247–1257 (1978).Google Scholar
  3. 3.
    V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5, 79–84 (1990); Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 115–119 (1991).Google Scholar
  4. 4.
    V. G. Bagrov, B. F. Samsonov, and A. V. Shapovalov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 2, 44–48, 102–105 (1991).Google Scholar
  5. 5.
    E. G. Kalnins, W. Miller Jr., Trans. AMS,244, 241–261 (1978).Google Scholar
  6. 6.
    E. G. Kalnins, “Separation of variables for Riemannian spaces of constant curvature,” in: Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 28 (1986).Google Scholar
  7. 7.
    L. P. Eisenhart, Ann. Math.,35, No. 2, 284–305 (1934).Google Scholar
  8. 8.
    M. S. Yarov-Yarovoi, Pril. Mat. Mekh.,27, 973–987 (1963).Google Scholar
  9. 9.
    V. N. Shapovalov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5, pp. 116–122 (1978); Izv. Vyssh. Uchebn. Zaved., Fiz., No. 6, 7–10 (1978).Google Scholar
  10. 10.
    V. N. Shapovalov, Diff. Uravn.,16, No. 10, 1864–1874 (1980).Google Scholar
  11. 11.
    F. M. Morse and G. Feshbach, Methods of Theoretical Physics [Russian translation], Vol. 1, IL, Moscow (1958).Google Scholar
  12. 12.
    G. Darboux, Sur une Classe Remarcable de Courbe et de Surfaces Algebraiques et sur la Theorie des Imaginaries, Paris (1872).Google Scholar
  13. 13.
    G. Darboux, Principles of Analytical Geometry [Russian translation], GONTI, Moscow-Leningrad (1938).Google Scholar
  14. 14.
    L. P. Eisenhart, Riemannian Geometry [Russian translation], IL, Moscow (1948).Google Scholar
  15. 15.
    M. Bocher, Über die Reihenent Wickelungen den Potential Theorie, Leipzig (1894).Google Scholar
  16. 16.
    E. G. Kalnins, and W. Miller Jr., J. Math. Phys.,17, No. 3, 331–335 (1976).Google Scholar
  17. 17.
    B. A. Rosenfeld, Non-Euclidean Geometry [Russian translation], Gostekhisdat, Moscow (1955).Google Scholar
  18. 18.
    F. Klein, Higher Geometry [Russian translation], GONTI, Moscow-Leningrad (1939).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • V. G. Bagrov
  • B. F. Samsonov

There are no affiliations available

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