Parametrized curves in Lagrange Grassmannians

Abstract

Curves in Lagrange Grassmannians naturally appear when one studies Jacobi equations for extremals, associated with geometric structures on manifolds. We fix integers d i and consider curves Λ ( t ) for which at each t the derivatives of order ⩽ i of all curves of vectors ℓ ( t ) ∈ Λ ( t ) span a subspace of dimension d i . We will describe the construction of a complete system of symplectic invariants for such parametrized curves, satisfying a certain genericity assumption, and give applications to geometric structures, including sub-Riemannian and sub-Finslerian structures. To cite this article: I. Zelenko, C. Li, C. R. Acad. Sci. Paris, Ser. I 345 (2007).