We discuss the interplay between lagrangian distributions and connections in (generalized) 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. © 2013.
Forger, M., & Yepes, S. Z. (2013). Lagrangian distributions and connections in multisymplectic and polysymplectic geometry. Differential Geometry and Its Application, 31(6), 775–807. https://doi.org/10.1016/j.difgeo.2013.09.004