On Liouville forms

Paulette Libermann

Banach Center Publications (2000)

  • Volume: 51, Issue: 1, page 151-164
  • ISSN: 0137-6934

Abstract

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We give different notions of Liouville forms, generalized Liouville forms and vertical Liouville forms with respect to a locally trivial fibration π:E → M. These notions are linked with those of semi-basic forms and vertical forms. We study the infinitesimal automorphisms of these forms; we also investigate the relations with momentum maps.

How to cite

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Libermann, Paulette. "On Liouville forms." Banach Center Publications 51.1 (2000): 151-164. <http://eudml.org/doc/209026>.

@article{Libermann2000,
abstract = {We give different notions of Liouville forms, generalized Liouville forms and vertical Liouville forms with respect to a locally trivial fibration π:E → M. These notions are linked with those of semi-basic forms and vertical forms. We study the infinitesimal automorphisms of these forms; we also investigate the relations with momentum maps.},
author = {Libermann, Paulette},
journal = {Banach Center Publications},
keywords = {generalized Liouville forms; vertical Liouville forms; locally trivial fibration; infinitesimal automorphisms; momentum maps},
language = {eng},
number = {1},
pages = {151-164},
title = {On Liouville forms},
url = {http://eudml.org/doc/209026},
volume = {51},
year = {2000},
}

TY - JOUR
AU - Libermann, Paulette
TI - On Liouville forms
JO - Banach Center Publications
PY - 2000
VL - 51
IS - 1
SP - 151
EP - 164
AB - We give different notions of Liouville forms, generalized Liouville forms and vertical Liouville forms with respect to a locally trivial fibration π:E → M. These notions are linked with those of semi-basic forms and vertical forms. We study the infinitesimal automorphisms of these forms; we also investigate the relations with momentum maps.
LA - eng
KW - generalized Liouville forms; vertical Liouville forms; locally trivial fibration; infinitesimal automorphisms; momentum maps
UR - http://eudml.org/doc/209026
ER -

References

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  1. [A.G.M] D. Alekseevsky, J. Grabowski, G. Marmo and P.W Michor, Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions, J. Math. Phys. 35 (1994) 4909-4927. Zbl0822.58016
  2. [A] V. Arnold, Mathematical methods of classical mechanics, Mir, Moscow 1975, Springer graduate texts in Math. No. 60. Springer-Verlag, New York. 
  3. [D.L.M] P. Dazord, A. Lichnerowicz and C.-M. Marle, Structure locale des variétés de Jacobi, J. Math. Pures et Appl. 70 (1991), 101-152. Zbl0659.53033
  4. [D.S] P. Dazord and D. Sondaz, Variétés de Poisson - algébroïdes de Lie, Université Claude Bernard Lyon 1. Publications du département de mathématiques, nouvelle série 1/B (1988), 1-68. 
  5. [G] C. Godbillon, Géométrie différentielle et mécanique classique, Hermann, Paris, 1969. Zbl0174.24602
  6. [K] M. Kummer, On the construction of the reduced phase space of a Hamiltonian system with symmetry, Indiana University Math. J. 30 (1981), 281-291. Zbl0425.70019
  7. [L1] P. Libermann, Problèmes d'équivalence et Géométrie symplectique, Proc IIIe rencontre de Géom. Schnepfenried, Astérisque 107-108 (1983), 43-68. Zbl0529.53030
  8. [L2] P. Libermann, Cartan-Darboux theorems for Pfaffian forms on foliated manifolds, Proc. VIth Int. Colloq. Diff. Geom. Santiago (1989), 125-144. 
  9. [L.M] P. Libermann and C.-M. Marle, Symplectic Geometry and Analytical Mechanics, Reidel, Dordrecht,1987. Zbl0643.53002
  10. [R] G. Reeb, Sur les espaces de Finsler et les espaces de Cartan, Colloque C.N.R.S. Géom. différentielle Strasbourg 1953, 35-40, Editions du CNRS Paris, 1953. Zbl0087.36801
  11. [W] A. Weinstein, A universal phase space for particles in Yang-Mills field, Letters in Math. Phys. 2 (1978), 417-420. Zbl0388.58010

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