Systems of conservation laws within the framework of the projective theoryof congruences: the Levy transformations of semi-Hamiltonian systems

We continue the investigation of the recently proposed geometric correspond ence between systems of conservation laws and congruences of lines in proje ctive space. The relationship between the 'additional' conservation laws an d hypersurfaces conjugate to a congruence is established, thus providing a basis for the Levy transformations of semi-Hamiltonian systems. Similarly, the correspondence between commuting flows and certain families of planes ( containing the lines of the congruence) gives rise to the adjoint Levy tran sformations.