FERAPONTOV.pdf (171.07 kB)
Integrable 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.
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. 17-32Publisher
© Cambridge University PressVersion
- VoR (Version of Record)
Publication date
2005Notes
This article was published in Glasgow Mathematical Journal [© Cambridge University Press]. The definitive version is available at: http://journals.cambridge.org/action/displayJournal?jid=GMJISSN
0017-0895Publisher version
Language
- en