  The goal of this paper is to extend to two-dimensional optimal control
systems with scalar input the classical notion of Gaussian curvature of
two-dimensional Riemannian surface using the Cartan's moving frame method. This
notion was already introduced by A. A. Agrachev and R. V. Gamkrelidze for more
general control systems using a purely variational approach. Then we will see
that the ``control'' analogue to Gaussian curvature reflects similar intrinsic
properties of the extremal flow. In particular if the curvature is negative,
arbitrarily long segment of extremals are locally optimal. Finally, we will
define and characterize flat control systems.
