Symplectic packings and algebraic geometry. (with an Appendix by Y. Karshon).
Given a symplectic fibration , with compact and symplectic and the fibres complex projective, we produce symplectic submanifolds of analytic in the vertical direction, and apply this to complex vector bundles on symplectic manifolds.
Horizontal systems of rays arise in the study of integral curves of Hamiltonian systems on T*X, which are tangent to a given distribution V of hyperplanes on X. We investigate the local properties of systems of rays for general pairs (H,V) as well as for Hamiltonians H such that the corresponding Hamiltonian vector fields are horizontal with respect to V. As an example we explicitly calculate the space of horizontal geodesics and the corresponding systems of rays for the canonical distribution...