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Monge-Ampere Systems with Lagrangian Pairs

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Title: Monge-Ampere Systems with Lagrangian Pairs
Authors: Ishikawa, Goo Browse this author
Machida, Yoshinori Browse this author
Keywords: Hessian Monge-Ampere equation
non-degenerate three form
bi-Legendrian fibration
Lagrangian contact structure
geometric structure
simple graded Lie algebra
Issue Date: 27-Nov-2015
Publisher: Institute of Mathematics of the National Academy of Sciences of Ukraine
Journal Title: Symmetry integrability and geometry-methods and applications
Volume: 11
Start Page: 81
Publisher DOI: 10.3842/SIGMA.2015.081
Abstract: The classes of Monge-Ampere systems, decomposable and bi-decomposable Monge-Ampere 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-Ampere 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-Ampere systems respectively in terms of the geometric structure and we show that these estimates are sharp (Proposition 4.2 and Theorem 5.3).
Type: article
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

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