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Monge-Ampere Systems with Lagrangian Pairs

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タイトル: Monge-Ampere Systems with Lagrangian Pairs
著者: Ishikawa, Goo 著作を一覧する
Machida, Yoshinori 著作を一覧する
キーワード: Hessian Monge-Ampere equation
non-degenerate three form
bi-Legendrian fibration
Lagrangian contact structure
geometric structure
simple graded Lie algebra
発行日: 2015年11月27日
出版者: Institute of Mathematics of the National Academy of Sciences of Ukraine
誌名: Symmetry integrability and geometry-methods and applications
巻: 11
開始ページ: 81
出版社 DOI: 10.3842/SIGMA.2015.081
抄録: 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).
資料タイプ: article
URI: http://hdl.handle.net/2115/60246
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

 

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