General Relativity and Gravitation

, Volume 42, Issue 10, pp 2525–2528 | Cite as

Editorial note to: Władysław Ślebodziński, On Hamilton’s canonical equations

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Golden Oldie Editorial


Tensor calculus Lie derivative of a tensor field Integral invariants Golden Oldie 



I would like to thank Professors Andrzej Trautman and Andrzej Krasinski for their helpful comments made while I was preparing this text for publication.

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This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution,and reproduction in any medium, provided the original author(s) and source are credited.


  1. 1.
    Hilbert, D.: Die Grundlagen der Physik (Erste Mitteilung). Nachr. Göttingen (1915), pp. 395–407Google Scholar
  2. 2.
    Cartan, É.: Leçons sur les invariants intégraux, based on lectures given in 1920–21 in Paris. Hermann, Paris (1922). Reprinted in 1958Google Scholar
  3. 3.
    van Dantzig, D.: Zur allgemeinen projektiven Differentialgeometrie. Proc. Roy. Acad. Amsterdam 35 Part I, 524–534; Part II, 535–542 (1932)Google Scholar
  4. 4.
    Lichnerowicz A.: Géométrie des groupes de transformations. Dunod, Paris (1958)MATHGoogle Scholar
  5. 5.
    Marsden J.E., Ratiu T.S.: Introduction to Mechanics and Symmetry. 2nd edn. Springer-Verlag, New York (1999)MATHGoogle Scholar
  6. 6.
    Schouten J.A.: Ricci-Calculus. 2nd edn. Springer-Verlag, Berlin (1954)MATHGoogle Scholar
  7. 7.
    Poincaré H.: Les méthodes nouvelles de la Mécanique céleste, t. III. Gauthier-Villars, Paris (1899)Google Scholar
  8. 8.
    de Donder Th.: Théorie des invariants intégraux. Gauthier-Villars, Paris (1927)MATHGoogle Scholar
  9. 9.
    Yano K.: The Theory of Lie Derivatives and its Applications. North-Holland, Amsterdam (1955)Google Scholar
  10. 10.
    Olver P.J.: Applications of Lie Groups to Differential Equations. 2nd edn. Springer-Verlag, New York (1993)MATHGoogle Scholar
  11. 11.
    Kolář I., Michor P.W., Slovák J.: Natural Operations in Differential Geometry. Springer-Verlag, Berlin (1993)MATHGoogle Scholar
  12. 12.
    Trautman A.: Remarks on the history of the notion of Lie differentiation. In: Krupková, O., Saunders, D.J. (eds) Variations, Geometry and Physics, Nova Science Publishers, New York (2008)Google Scholar
  13. 13.
    Ślebodziński W.: Sur les equations de Hamilton. Bull. Acad. Roy. de Belg. 17, 864–870 (1931)Google Scholar
  14. 14.
    van Dantzig D.: One the thermo-hydrodynamics of perfectly perfect fluids. Nederl. Akad. Wetensch. Proc. 43, 157–171 (1940)Google Scholar

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© The Author(s) 2010

Authors and Affiliations

  1. 1.Instytut Fizyki TeoretycznejUniwersytet WarszawskiWarsawPoland

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