open access

https://hdl.handle.net/2115/60246

Monge-Ampere Systems with Lagrangian Pairs

英語

simple graded Lie algebra

2015-11-27

Institute of Mathematics of the National Academy of Sciences of Ukraine

Symmetry integrability and geometry-methods and applications

11

81

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).

学術雑誌論文

Version of Record

Creative Commons Attribution-ShareAlike 4.0 Internationa

1815-0659