Contact geometry of multidimensional Monge-Ampere equations: characteristics, intermediate integrals and solutions

@article{Alekseevsky2010ContactGO,
  title={Contact geometry of multidimensional Monge-Ampere equations: characteristics, intermediate integrals and solutions},
  author={D. Alekseevsky and R. Alonso-Blanco and G. Manno and F. Pugliese},
  journal={Annales de l'Institut Fourier},
  year={2010},
  volume={62},
  pages={497-524}
}
We study the geometry of multidimensional scalar 2 order PDEs (i.e. PDEs with n independent variables) with one unknown function, viewed as hypersurfaces E in the Lagrangian Grassmann bundle M (1) over a (2n + 1)-dimensional contact manifold (M, C). We develop the theory of characteristics of the equation E in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of E . After specifying the results to general Monge… Expand
Contact manifolds, Lagrangian Grassmannians and PDEs
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