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Integrable four-component systems of conservation laws and linear congruences in ${\mathbb P}^5$

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posted on 17.02.2009, 13:14 authored by Evgeny FerapontovEvgeny Ferapontov, S.I. Agafonov
We 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.

History

School

  • Science

Department

  • Mathematical Sciences

Citation

FERAPONTOV, E.V. and AGAFONOV, S.I., 2005. Integrable four-component systems of conservation laws and linear congruences in ${\mathbb P}^5$. Glasgow Mathematical Journal, 47 (A), pp. 17-32

Publisher

© Cambridge University Press

Version

VoR (Version of Record)

Publication date

2005

Notes

This article was published in Glasgow Mathematical Journal [© Cambridge University Press]. The definitive version is available at: http://journals.cambridge.org/action/displayJournal?jid=GMJ

ISSN

0017-0895

Language

en