Generalized geometrical structures of odd dimensional manifolds (Q1006625)

This paper studies geometrical structures on the phase space of a space-time naturally induced by a metric and a phase connection. The authors first recall some standard structures; then introduce both an almost-cosymplectic-contact structure and an almost-coPoisson-Jacobi structure. These notions generalize the contact structure on a odd dimensional manifold and the Jacobi structure respectively. The general properties of these new structures are then studied. Examples are finally given. In particular, the authors present geometrical dynamical structures on the phase space of a general relativistic particle, regarded as the first jet space of motions in a spacetime.