An Inverse Problem from Sub-riemannian Geometry

نویسندگان

  • Thomas A. Ivey
  • THOMAS A. IVEY
چکیده

The geodesics for a sub-Riemannian metric on a threedimensional contact manifold M form a 1-parameter family of curves along each contact direction. However, a collection of such contact curves on M , locally equivalent to the solutions of a fourth-order ODE, are the geodesics of a sub-Riemannian metric only if a sequence of invariants vanish. The first of these, which was first identified by Fels, determines if the differential equation is variational. The next two determine if there is a well-defined metric on M and if the given paths are its geodesics.

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تاریخ انتشار 2001