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dc.contributor.author Ishikawa, G.
dc.contributor.author Machida, Y.
dc.date.accessioned 2019-02-13T17:48:28Z
dc.date.available 2019-02-13T17:48:28Z
dc.date.issued 2015
dc.identifier.citation Monge-Ampère Systems with Lagrangian Pairs / G. Ishikawa, Y. Machida // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 31 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 58K20; 53A15; 53C42
dc.identifier.other DOI:10.3842/SIGMA.2015.081
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/147154
dc.description.abstract The classes of Monge-Ampère systems, decomposable and bi-decomposable Monge-Ampère systems, including equations for improper affine spheres and hypersurfaces of constant Gauss-Kronecker curvature are introduced. They are studied by the clear geometric setting of Lagrangian contact structures, based on the existence of Lagrangian pairs in contact structures. We show that the Lagrangian pair is uniquely determined by such a bi-decomposable system up to the order, if the number of independent variables ≥3. We remark that, in the case of three variables, each bi-decomposable system is generated by a non-degenerate three-form in the sense of Hitchin. It is shown that several classes of homogeneous Monge-Ampère systems with Lagrangian pairs arise naturally in various geometries. Moreover we establish the upper bounds on the symmetry dimensions of decomposable and bi-decomposable Monge-Ampère systems respectively in terms of the geometric structure and we show that these estimates are sharp (Proposition 4.2 and Theorem 5.3). uk_UA
dc.description.sponsorship The first author was partially supported by Grants-in-Aid for Scientific Research No. 19654006. The second author was partially supported by Grants-in-Aid for Scientific Research (C) No. 18540105. The authors would like to thank anonymous referees for the valuable comments to improve the paper. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Monge-Ampère Systems with Lagrangian Pairs uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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