00974nas a2200121   4500008004300000245004200043210004200085260001300127520063300140100002500773700001800798856003600816       2000                        en_Ud  00aPrincipal invariants of Jacobi curves0 aPrincipal invariants of Jacobi curves  bSpringer3 aJacobi curves are far going generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. Differential geometry of these curves provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric  structures. In the present paper we mainly discuss two principal invariants: the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmanian providing the curve with a natural projective structure, and a fundamental form, which is a 4-oder differential on the curve.1 aAgrachev, Andrei, A.1 aZelenko, Igor  uhttp://hdl.handle.net/1963/3825