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Title: | Integrable four-component systems of conservation laws and linear congruences in ${\mathbb P}^5$ |
Authors: | Ferapontov, E.V. Agafonov, S.I. |
Issue Date: | 2005 |
Publisher: | © Cambridge University Press |
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 |
Abstract: | 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. |
Description: | 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 |
Version: | Published |
DOI: | 10.1017/S0017089505002259 |
URI: | https://dspace.lboro.ac.uk/2134/4237 |
Publisher Link: | http://dx.doi.org/10.1017/S0017089505002259 |
ISSN: | 0017-0895 |
Appears in Collections: | Published Articles (Maths)
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