Transformations of quasilinear systems originating from the projective theory of congruences

Details Transformations of quasilinear systems originating from the projective theory of congruences Transformations of quasilinear systems originating from the projective theory of congruences

1999-04-30

arxiv.org/abs/math/9904170v1

Mathematics

Differential Geometry

Latex

Scientific paper

We continue the investigation of the correspondence between systems of conservation laws and congruences of lines in projective space. Relationship between "additional" conservation laws and hypersurfaces conjugate to a congruence is established. This construction allows us to introduce, in a purely geometric way, the L\'evy transformations of semihamiltonian systems. Correspondence between commuting flows and certain families of planes containing the lines of the congruence is pointed out. In the particular case n=2 this construction provides an explicit parametrization of surfaces, harmonic to a given congruence. Adjoint L\'evy transformations of semihamiltonian systems are discussed. Explicit formulae for the L\'evy and adjoint L\'evy transformations of the characteristic velocities are set down. A closely related construction of the Ribaucour congruences of spheres is discussed in the Appendix.

Affiliated with

Also associated with

No associations

Rating

Transformations of quasilinear systems originating from the projective theory of congruences does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Transformations of quasilinear systems originating from the projective theory of congruences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transformations of quasilinear systems originating from the projective theory of congruences will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-158606