Janusz Grabowski
Contact geometry as a chapter in symplectic geometry
I will present an approach to the contact geometry which, in contrast to the one dominating in the physics literature, serves also for non-trivial contact structures. In this approach contact geometry is not an ‘odd-dimensional cousin’ of symplectic geometry, but rather a part of the latter, namely ‘homogeneous symplectic geometry’. This understanding of contact structures has a long tradition and taken seriously is very effective in applications. Instead of ad hoc definitions in the contact case, we have therefore obvious concepts coming directly from the standard symplectic picture. In particular, the contact Hamiltonian Mechanics, extensively studied nowadays, can be fully expressed in terms of the traditional symplectic one, and Legendre submanifolds turn out to be Lagrangian. Also a natural understanding of contact reductions with respect to group actions comes easily from the Marsden-Weinstein-Meyer symplectic reduction.
