TY - CHAP T1 - Principal invariants of Jacobi curves T2 - Nonlinear control in the Year 2000 / Alberto Isidori, Francoise Lamnabhi-Lagarrigue, Witold Respondek (eds.) - Springer : Berlin, 2001. - (Lecture notes in control and information sciences ; 258). - ISBN 1-85233-363-4 (v. 1). - p. 9-22. Y1 - 2000 A1 - Andrei A. Agrachev A1 - Igor Zelenko AB - Jacobi 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. JF - Nonlinear control in the Year 2000 / Alberto Isidori, Francoise Lamnabhi-Lagarrigue, Witold Respondek (eds.) - Springer : Berlin, 2001. - (Lecture notes in control and information sciences ; 258). - ISBN 1-85233-363-4 (v. 1). - p. 9-22. PB - Springer UR - http://hdl.handle.net/1963/3825 U1 - 502 U2 - Mathematics U3 - Functional Analysis and Applications ER -