# A Geometry for Second-Order PDEs and their Integrability, Part I

@article{Smith2010AGF, title={A Geometry for Second-Order PDEs and their Integrability, Part I}, author={Abraham Smith}, journal={arXiv: Differential Geometry}, year={2010} }

For the purpose of understanding second-order scalar PDEs and their hydrodynamic integrability, we introduce G-structures that are induced on hypersurfaces of the space of symmetric matrices (interpreted as the fiber of second-order jet space) and are defined by non-degenerate scalar second-order-only (Hessian) PDEs in any number of variables. The fiber group is a conformal orthogonal group that acts on the space of independent variables, and it is a subgroup of the conformal orthogonal group… Expand

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