Monge-Ampère Systems with Lagrangian Pairs
Monge-Ampère Systems with Lagrangian Pairs
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 …