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dc.contributor.authorDoubrov, Boris
dc.contributor.authorMedvedev, Alexandr
dc.contributor.authorThe, Dennis
dc.date.accessioned2019-08-13T13:27:25Z
dc.date.available2019-08-13T13:27:25Z
dc.date.embargoEndDate2020-07-04
dc.date.issued2019-07-04
dc.description.abstractWe consider Legendrian contact structures on odd-dimensional complex analytic manifolds. We are particularly interested in integrable structures, which can be encoded by compatible complete systems of second order PDEs on a scalar function of many independent variables and considered up to point transformations. Using the techniques of parabolic differential geometry, we compute the associated regular, normal Cartan connection and give explicit formulas for the harmonic part of the curvature. The PDE system is trivializable by means of point transformations if and only if the harmonic curvature vanishes identically. In dimension five, the harmonic curvature takes the form of a binary quartic field, so there is a Petrov classification based on its root type. We give a complete local classification of all five-dimensional integrable Legendrian contact structures whose symmetry algebra is transitive on the manifold and has at least one-dimensional isotropy algebra at any point.en_US
dc.description.sponsorshipARC Discovery Grant Austrian Science Fund (FWF)en_US
dc.descriptionThis is a post-peer-review, pre-copyedit version of an article published in the <i>Journal of Geometric Analysis</i>. The final authenticated version is available online at: <a href=https://doi.org/10.1007/s12220-019-00219-x>https://doi.org/10.1007/s12220-019-00219-x</a>.en_US
dc.identifier.citationDoubrov, B., Medvedev, A. & The, D. (2019). Homogeneous integrable Legendrian contact structures in dimension five. <i>Journal of Geometric Analysis</i>. https://doi.org/10.1007/s12220-019-00219-xen_US
dc.identifier.issn1050-6926
dc.identifier.issn1559-002X
dc.identifier.otherFRIDAID 1711236
dc.identifier.otherhttps://doi.org/10.1007/s12220-019-00219-x
dc.identifier.urihttps://hdl.handle.net/10037/15904
dc.language.isoengen_US
dc.publisherSpringeren_US
dc.relation.journalJournal of Geometric Analysis
dc.rights.accessRightsembargoedAccessen_US
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410::Topology/geometry: 415en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Topologi/geometri: 415en_US
dc.subjectLegendrian structuresen_US
dc.subjectSymmetry algebraen_US
dc.subjectCurvature moduleen_US
dc.subjectMultiply transitiveen_US
dc.subjectComplete systems of PDEsen_US
dc.titleHomogeneous integrable Legendrian contact structures in dimension fiveen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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