Reduction of manifolds of rational curves and related problems of the theory of differential equations (Q1082614)

A generalization of the method of characteristics for the integration of nonlinear differential equations is built. The method is applied to the description of those families of rational curves on a manifold that can be realised as full families on a modified manifold. The meaning of this problem for integral geometry, and for the construction of Hamiltonians with rational rays, and for the integration of self-dual Einstein and Yang-Mills equations is discussed.