1202.5054 (Michael Forger et al.)

Lagrangian Distributions and Connections in Symplectic Geometry    [PDF]

Michael Forger, Sandra Z. Yepes

We discuss the interplay between lagrangian distributions and connections in
symplectic geometry, beginning with the traditional case of symplectic
manifolds and then passing to the more general context of poly- and
multisymplectic structures on fiber bundles, which is relevant for the
covariant hamiltonian formulation of classical field theory. In particular, we
generalize Weinstein's tubular neighborhood theorem for symplectic manifolds
carrying a (simple) lagrangian foliation to this situation. In all cases, the
Bott connection, or an appropriately extended version thereof, plays a central
role.

View original: http://arxiv.org/abs/1202.5054