Skip to main content

Liouville Forms, Parallelisms and Cartan Connections

  • Conference paper
Book cover Jean Leray ’99 Conference Proceedings

Part of the book series: Mathematical Physics Studies ((MPST,volume 24))

  • 316 Accesses

Abstract

This paper is a survey (without proofs) of subjects connected with the title. It does not deal directly with Mechanics but investigates tools utilized in Analytical Mechanics. For a direct treatment see the contribution of C. Marle to this publication [12].

Cet article est dédié à la mémoire de Jean Leray en témoignage d’admiration

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albert, C. and Dazord, P., Groupoïdes de Lie et groupoïdes symplectiques, M.S.R.I. Berkeley Publications, vol. 20, 1989; Publications dépt. Math. Lyon, Nouvelle série 1990.

    Google Scholar 

  2. Alekseevsky, D., Grabowski, J., Marmo, G., and Michor, P.W., Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions, J. Math. Phys. 35 (1994), 4909 – 4924.

    Article  MathSciNet  MATH  Google Scholar 

  3. Condevaux, M., Dazord, P., and Molino, P., Géométrie du moment, Publications dépt. math. Lyon, Nouvelle série 1983, 131 – 160.

    Google Scholar 

  4. Ehresmann, Ch., Les connexions infinitésimales, Colloq. Topologie (Bruxelles 1950). Œvres complètes, Partie 12, 179 – 205.

    Google Scholar 

  5. Kobayashi, S., Transformations groups in differential geometry, Springer–Verlag, Berlin, Heidelberg, New York 1972.

    Google Scholar 

  6. Kummer, M., On the construction of the reduced phase of a Hamiltonian system with symmetry, Indiana University math. J. 30 (1981), 281 – 291.

    Article  MathSciNet  MATH  Google Scholar 

  7. Lazard, M., Leçons de calcul différentiel et intégral dans les variétés banachiques, unpublished 1970.

    Google Scholar 

  8. Libermann, P., Parallélismes, Journ. of Diff. Geom. (4) 8 (1973), 511 – 539.

    MathSciNet  MATH  Google Scholar 

  9. Libermann, P., Parallélismes, Problèmes d’équivalence et géométrie symplectique, Proc. IIIe rencontre de Geom. Schnepfenried, Astérisque 107–108 1983, 43–68. Cartan-Darboux theorems for Pfaffian forms on foliated manifolds, Proc. VIth Int. Colloq. Diff. Geom. Santiago 1989, 125–144.

    Google Scholar 

  10. Libermann, P. and Marle, C.-M., On Liouville forms, Banach Center publications, vol. 51, 2000, Institute of Mathematics, Polish Academy of Sciences, Warszawa.

    Google Scholar 

  11. Libermann, P. and Marle, C.-M., Symplectic geometry and analytical mechanics, D. Reidel Publishing Company, Dordrecht 1987.

    Google Scholar 

  12. Marle, C.-M., On mechanical systems with a Lie group as configuration space.

    Google Scholar 

  13. Weinstein, A., A universal phase space for particles in Yang–Mills field, Letters Math. Phys. 2 (1978), 417 – 420.

    Article  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Libermann, P. (2003). Liouville Forms, Parallelisms and Cartan Connections. In: de Gosson, M. (eds) Jean Leray ’99 Conference Proceedings. Mathematical Physics Studies, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2008-3_28

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-2008-3_28

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6316-8

  • Online ISBN: 978-94-017-2008-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics