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math.DG2017
Involutive Tableaux, Characteristic Varieties, and Rank-one Varieties in the Geometric Study of PDEs
Abraham D. Smith
This expository monograph cuts a short path from the common, elementary background in geometry (linear algebra, vector bundles, and algebraic ideals) to the most advanced theorems…
math.DG2010★ 3 cited
A Geometry for Second-Order PDEs and their Integrability, Part I
Abraham D. Smith
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 symmetri…
math.DG2009
Integrable GL(2) Geometry and Hydrodynamic Partial Differential Equations
Abraham D. Smith
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…