%0 Book Section %B 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. %D 2000 %T Principal invariants of Jacobi curves %A Andrei A. Agrachev %A Igor Zelenko %X 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. %B 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. %I Springer %G en_US %U http://hdl.handle.net/1963/3825 %1 502 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-22T10:28:35Z\\nNo. of bitstreams: 1\\nagrachevzelenkojac.pdf: 183303 bytes, checksum: dfda52156443588909812f02012c2883 (MD5) %R 10.1007/BFb0110204