2001/06/05 by Sergey I. Agafonov, S. I. Agafonov, Agafonov, S. I. +2
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.DG
paper · pdf · doi:10.48550/arxiv.math/0106028
26 pages
arxiv created 2001/06/05 · openalex publication_date 2001/06/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a geometric correspondence between (a) linearly degenerate systems of conservation laws with rectilinear rarefaction curves and (b) congruences of lines in projective space whose developable surfaces are planar pencils of lines. We prove that in projective 4-space such congruences are necessarily linear. Based on the results of Castelnuovo, the classification of three-component systems is obtained, revealing a close relationship of the problem with projective geometry of the Veronese variety and the theory of associativity equations of two-dimensional topological field theory.