Controlling Hamiltonian chaos via Gaussian curvature

We present a method allowing one to partly stabilize some chaotic Hamiltonians which have two degrees of freedom. The purpose of the method is to avoid the regions of V(q(1),q(2)) where its Gaussian curvature becomes negative. We show the stabilization of the Henon-Heiles system, over a wide area, for the critical energy E=1/6. Total energy of the system varies only by a few percent. [S1063-651X(99)50512-6].