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Download fileIntegrable four-component systems of conservation laws and linear congruences in ${\mathbb P}^5$
journal contribution
posted on 2009-02-17, 13:14 authored by Evgeny FerapontovEvgeny Ferapontov, S.I. AgafonovWe propose a differential-geometric classification of the fourcomponent
hyperbolic systems of conservation laws which satisfy the following properties:
(a) they do not possess Riemann invariants; (b) they are linearly degenerate;
(c) their rarefaction curves are rectilinear; (d) the cross-ratio of the four characteristic
speeds is harmonic. This turns out to provide a classification of projective congruences
in ${\mathbb P}^5$ whose developable surfaces are planar pencils of lines, each of these
lines cutting the focal variety at points forming a harmonic quadruplet. Symmetry
properties and the connection of these congruences to Cartan’s isoparametric hypersurfaces
are discussed.
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