# Integrable GL(2) Geometry and Hydrodynamic Partial Differential Equations

@article{Smith2009IntegrableGG, title={Integrable GL(2) Geometry and Hydrodynamic Partial Differential Equations}, author={A. Smith}, journal={arXiv: Differential Geometry}, year={2009} }

This article is a local analysis of integrable GL(2)-structures of degree 4. A GL(2)-structure of degree n corresponds to a distribution of rational normal cones over a manifold M of dimension (n+1). Integrability corresponds to the existence of many submanifolds that are spanned by lines in the cones. These GL(2)-structures are important because they naturally arise from a certain family of second-order hyperbolic PDEs in three variables that are integrable via hydrodynamic reduction. Familiar… Expand

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