Natural transformations of symplectic structures into Poisson's and Jacobi's brackets
Archivum mathematicum, Tome 34 (1998) no. 4, pp. 505-515
A complete classification of natural transformations of symplectic structures into Poisson's brackets as well as into Jacobi's brackets is given.
A complete classification of natural transformations of symplectic structures into Poisson's brackets as well as into Jacobi's brackets is given.
Classification :
53D05, 53D17
Keywords: natural operator; symplectic manifold; Poisson manifold; Jacobi manifold
Keywords: natural operator; symplectic manifold; Poisson manifold; Jacobi manifold
@article{ARM_1998_34_4_a8,
author = {D\k{e}becki, Jacek},
title = {Natural transformations of symplectic structures into {Poisson's} and {Jacobi's} brackets},
journal = {Archivum mathematicum},
pages = {505--515},
year = {1998},
volume = {34},
number = {4},
mrnumber = {1679644},
zbl = {0966.53052},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ARM_1998_34_4_a8/}
}
Dębecki, Jacek. Natural transformations of symplectic structures into Poisson's and Jacobi's brackets. Archivum mathematicum, Tome 34 (1998) no. 4, pp. 505-515. http://geodesic.mathdoc.fr/item/ARM_1998_34_4_a8/
[1] Dȩbecki J.: Invariant vector fields of Hamiltonians. Archivum Mathematicum (Brno) 34 (1998), 295-300. | MR
[2] Kolář I., Michor P. W., Slovák J.: Natural operations in differential geometry. Springer-Verlag, 1993. | MR | Zbl
[3] Peetre J.: Une caractérisation abstraite des opérateurs différentiels. Math. Scand. 7 (1959), 211-218. | MR | Zbl
[4] Peetre J.: Réctification a l’article “Une caractérisation abstraite des opérateurs différentiels”. Math. Scand. 8 (1960), 116-120. | MR | Zbl
[5] Vaisman I.: Lectures on the Geometry of Poisson Manifolds. Birkhäuser, Basel–Boston–Berlin, 1994. | MR | Zbl