Janusz Grabowski, Pawel Urbanski
Tangent Lifts of Poisson and Related Structures
The paper is published: J. Physics A: Math. Gen. 28 (1995) 6743-6777

MSC:

58F05 Hamiltonian and Lagrangian systems; symplectic geometry, See also {70Hxx, 81S10}

53C12 Foliations (differential geometric aspects), See Also {57R30, 57R32}

53C15 General geometric structures on manifolds (almost complex, contact, symplectic, almost product structures, etc.)

58A30 Vector distributions (subbundles of the tangent bundles)

70H15 Canonical transformations

PACS: 02.40+m,03.20+i
Abstract: The derivation $d_T$ on the exterior algebra of forms on a
manifold $M$ with values in the exterior algebra of forms on the
tangent bundle $TM$ is extended to multivector fields.
These tangent lifts are studied with applications to the theory of
Poisson structures, canonical vector fields and Poisson-Lie groups.
Keywords: tangent bundle, vector field, differential form, Poisson structure, Lagrangian submanifold, canonical transformation, foliation, Poisson-Lie group
Notes: second version