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We present a generalization of Penrose’s twistor theory based on the geometry of rational curves in complex manifolds. The analytical counterpart of this complex geometry consists, in the three simplest cases, of a system of differential equations closely connected with Einstein’s equations.
We have considered all nonlinear evolution equations generated by the operator relation where L is the differential operator of the form and A, B are rationally dependent on parameter η differential operators. We have found the infinite dimensional group of symmetries of equations thus obtained. Several infinite series of conservation laws are also found which are satisfied by the solutions of these...
Recent results on the relativistic mechanics of directly interacting point particles are reviewed. A reparametrization invariant formulation of the problem is given in terms of projective tangent spaces and second order differential systems. The relation between this general approach and the phase space constraint Hamiltonian picture (including the theorem about gauge dependence of world lines for...
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