On submanifolds and quotients of Poisson and Jacobi manifolds

Charles-Michel Marle

Banach Center Publications (2000)

  • Volume: 51, Issue: 1, page 197-209
  • ISSN: 0137-6934

Abstract

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We obtain conditions under which a submanifold of a Poisson manifold has an induced Poisson structure, which encompass both the Poisson submanifolds of A. Weinstein [21] and the Poisson structures on the phase space of a mechanical system with kinematic constraints of Van der Schaft and Maschke [20]. Generalizations of these results for submanifolds of a Jacobi manifold are briefly sketched.

How to cite

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Marle, Charles-Michel. "On submanifolds and quotients of Poisson and Jacobi manifolds." Banach Center Publications 51.1 (2000): 197-209. <http://eudml.org/doc/209031>.

@article{Marle2000,
abstract = {We obtain conditions under which a submanifold of a Poisson manifold has an induced Poisson structure, which encompass both the Poisson submanifolds of A. Weinstein [21] and the Poisson structures on the phase space of a mechanical system with kinematic constraints of Van der Schaft and Maschke [20]. Generalizations of these results for submanifolds of a Jacobi manifold are briefly sketched.},
author = {Marle, Charles-Michel},
journal = {Banach Center Publications},
keywords = {submanifold; Poisson manifold; Poisson structure; mechanical system; phase space},
language = {eng},
number = {1},
pages = {197-209},
title = {On submanifolds and quotients of Poisson and Jacobi manifolds},
url = {http://eudml.org/doc/209031},
volume = {51},
year = {2000},
}

TY - JOUR
AU - Marle, Charles-Michel
TI - On submanifolds and quotients of Poisson and Jacobi manifolds
JO - Banach Center Publications
PY - 2000
VL - 51
IS - 1
SP - 197
EP - 209
AB - We obtain conditions under which a submanifold of a Poisson manifold has an induced Poisson structure, which encompass both the Poisson submanifolds of A. Weinstein [21] and the Poisson structures on the phase space of a mechanical system with kinematic constraints of Van der Schaft and Maschke [20]. Generalizations of these results for submanifolds of a Jacobi manifold are briefly sketched.
LA - eng
KW - submanifold; Poisson manifold; Poisson structure; mechanical system; phase space
UR - http://eudml.org/doc/209031
ER -

References

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  21. [21] A. Weinstein, The local structure of Poisson manifolds, J. Differential Geometry 18 (1983), 523-557 and 22 (1985), 255. Zbl0524.58011

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