基于投影同余理论的拟线性系统变换
Transformations of quasilinear systems originating from the projective theory of congruences
摘要：
我们继续研究射影空间中守恒律系统与线汇之间的对应关系。建立了“附加”守恒律与共轭于同余的超曲面之间的关系。这种构造允许我们以纯粹几何的方式引入半哈密顿系统的Lévy变换。对应之间的交换流和某些家庭的飞机包含线的合同指出。在n=2的特殊情况下，这种构造提供了一个明确的参数化的表面，谐波到一个给定的同余。讨论了半Hamilton系统的伴随Lévy变换。给出了特征速度的Lévy变换和伴随Lévy变换的显式公式。一个密切相关的建设Ribaucour合同的领域是讨论在附录中。
英文摘要：
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 Lévy 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 Lévy transformations of semihamiltonian systems are discussed. Explicit formulae for the Lévy and adjoint Lévy transformations of the characteristic velocities are set down. A closely related construction of the Ribaucour congruences of spheres is discussed in the Appendix.
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