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$𝒟$ -modules, contact valued calculus and Poincaré-Cartan form

Ricardo J. Alonso Blanco — 1999

Czechoslovak Mathematical Journal

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

Dmitri V. Alekseevsky; Ricardo Alonso-Blanco; Gianni Manno; Fabrizio Pugliese — 2012

Annales de l’institut Fourier

We study the geometry of multidimensional scalar $2^{n d}$ order PDEs (i.e. PDEs with $n$ independent variables), viewed as hypersurfaces $ℰ$ in the Lagrangian Grassmann bundle $M^{(1)}$ over a $(2 n + 1)$ -dimensional contact manifold $(M, 𝒞)$ . We develop the theory of characteristics of $ℰ$ in terms of contact geometry and of the geometry of Lagrangian Grassmannian and study their relationship with intermediate integrals of $ℰ$ . After specializing such results to general Monge-Ampère...

The only global contact transformations of order two or more are point transformations.

Alonso-Blanco, Ricardo J.; Blázquez-Sanz, David — 2005

Journal of Lie Theory

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