Natural operations of Hamiltonian type on the cotangent bundle

Proceedings of the 16th Winter School "Geometry and Physics", GDML_Books, (1997), p. [81]-86 / Harvested from

Résumé

The authors study some geometrical constructions on the cotangent bundle $T^{*} M$ from the viewpoint of natural operations. First they deduce that all natural operators transforming functions on $T^{*} M$ into vector fields on $T^{*} M$ are linearly generated by the Hamiltonian vector field with respect to the canonical symplectic structure of $T^{*} M$ and by the Liouville vector field of $T^{*} M$ . Then they determine all natural operators transforming pairs of functions on $T^{*} M$ into functions on $T^{*} M$ . In this case, the main generator is the classical Poisson bracket.

MR MR1469023 | Zbl 0883.53036

EUDML-ID : urn:eudml:doc:221232
Mots clés:

@article{701597,
     title = {Natural operations of Hamiltonian type on the cotangent bundle},
     booktitle = {Proceedings of the 16th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1997},
     pages = {[81]-86},
     mrnumber = {MR1469023},
     zbl = {0883.53036},
     url = {http://dml.mathdoc.fr/item/701597}
}

Doupovec, Miroslav; Kurek, Jan. Natural operations of Hamiltonian type on the cotangent bundle, dans Proceedings of the 16th Winter School "Geometry and Physics", GDML_Books,  (1997), pp. [81]-86. http://gdmltest.u-ga.fr/item/701597/