Mathematics

Jacobi curves are the curves in the Lagrangian Grassmanian corresponding to a dynamical system. The differential geometry of these curves provides some basic symplectic invariants of the dynamical system such as the {\sl generalized curvature tensor } and the {\sl Ricci curvature}. In the present work we study the dependence of these invariants on the reduction in the phase space of the systems with symmetries. We also give some illustrating examples from classical mechanics.