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Keywords:
symplectic manifold; Hamiltonian lift; natural operator
symplectic manifold; Hamiltonian lift; natural operator
Summary:
A complete classification of natural transformations of Hamiltonians into vector fields on symplectic manifolds is given herein.
References:
[1] Dȩbecki J., Gancarzewicz J., de León M., Mikulski W.: Invariants of Lagrangians and their calssifications. J. Math. Phys., Vol. 35, No. 9, 1994, pp. 4568–4593. MR 1290890
[2] Dȩbecki J.: Natural transformations of Lagrangians into $p$-forms on the tangent bundle; Quantization, Coherent States, and Complex Structures. Plenum Publishing Corp., New York, 1995, pp. 141–146. MR 1403155
[3] Doupovec M., Kurek J.: Natural operations of Hamiltonian type on the cotangent bundle. Suppl. Rend. Circ. Mat. Palermo, Serie II 34 (1995).
[4] Kolář I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry. Springer-Verlag, Berlin, 1993. MR 1202431
[5] de León M., Rodrigues P. R.: Methods of Differential Geometry in Analytical Mechanics. North-Holland Math. Ser., Vol. 152, Amsterdam, 1989. MR 1021489
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