Geodesic
INTEGRABLE FOUR-COMPONENT SYSTEMS OF CONSERVATION LAWS AND LINEAR CONGRUENCES IN ${\mathbb P}^5$
Glasgow mathematical journal, Tome 47 (2005) no. A, pp. 17-32

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DOI

We propose a differential-geometric classification of the four-component 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.
DOI : 10.1017/S0017089505002259
Mots-clés : 53A25, 53B50, 35L65 
AGAFONOV, S. I.; FERAPONTOV, E. V. INTEGRABLE FOUR-COMPONENT SYSTEMS OF CONSERVATION LAWS AND LINEAR CONGRUENCES IN ${\mathbb P}^5$. Glasgow mathematical journal, Tome 47 (2005) no. A, pp. 17-32. doi: 10.1017/S0017089505002259
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     author = {AGAFONOV, S. I. and FERAPONTOV, E. V.},
     title = {INTEGRABLE {FOUR-COMPONENT} {SYSTEMS} {OF} {CONSERVATION} {LAWS} {AND} {LINEAR} {CONGRUENCES} {IN} ${\mathbb P}^5$},
     journal = {Glasgow mathematical journal},
     pages = {17--32},
     year = {2005},
     volume = {47},
     number = {A},
     doi = {10.1017/S0017089505002259},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089505002259/}
}
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