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dc.contributor.authorFerapontov, Evgeny V
dc.contributor.authorKruglikov, Boris
dc.date.accessioned2020-03-31T11:28:11Z
dc.date.available2020-03-31T11:28:11Z
dc.date.issued2019-10-08
dc.description.abstractParaconformal or GL(2, ℝ) geometry on an <i>n</i>-dimensional manifold <i>M</i> is defined by a field of rational normal curves of degree <i>n</i> – 1 in the projectivised cotangent bundle <i>ℙT*M</i>. Such geometry is known to arise on solution spaces of ODEs with vanishing Wünschmann (Doubrov–Wilczynski) invariants. In this paper we discuss yet another natural source of <i>GL</i>(2, ℝ) structures, namely dispersionless integrable hierarchies of PDEs such as the dispersionless Kadomtsev–Petviashvili (dKP) hierarchy. In the latter context, <i>GL</i>(2, ℝ) structures coincide with the characteristic variety (principal symbol) of the hierarchy.<p> <p>Dispersionless hierarchies provide explicit examples of particularly interesting classes of involutive <i>GL</i>(2, ℝ) structures studied in the literature. Thus, we obtain torsion-free <i>GL</i>(2, ℝ) structures of Bryant [5] that appeared in the context of exotic holonomy in dimension four, as well as totally geodesic <i>GL</i>(2, ℝ) structures of Krynski [33]. The latter possess a compatible affine connection (with torsion) and a two-parameter family of totally geodesic <i>α</i>-manifolds (coming from the dispersionless Lax equations), which makes them a natural generalisation of the Einstein–Weyl geometry. <p>Our main result states that involutive <i>GL</i>(2, ℝ) structures are governed by a dispersionless integrable system whose general local solution depends on 2<i>n</i> – 4 arbitrary functions of 3 variables. This establishes integrability of the system of Wünschmann conditions.en_US
dc.identifier.citationFerapontov EV, Kruglikov BS. Dispersionless integrable hierarchies and GL(2,R) geometry. Mathematical proceedings of the Cambridge Philosophical Society (Print). 2019en_US
dc.identifier.cristinIDFRIDAID 1745277
dc.identifier.doi10.1017/S0305004119000355
dc.identifier.issn0305-0041
dc.identifier.issn1469-8064
dc.identifier.urihttps://hdl.handle.net/10037/17940
dc.language.isoengen_US
dc.publisherCambridge University Press (CUP)en_US
dc.relation.journalMathematical proceedings of the Cambridge Philosophical Society (Print)
dc.rights.accessRightsopenAccessen_US
dc.rights.holder© Cambridge Philosophical Society 2019en_US
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410en_US
dc.titleDispersionless integrable hierarchies and GL(2,R) geometryen_US
dc.type.versionacceptedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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