Rank 2 distributions of Monge equations: symmetries, equivalences, extensions

2009/10/30 by Ian Anderson, Anderson, Ian, Boris Kruglikov +1 · 1 citation
Mathematics · Physics and Astronomy · #34C14 #35A30 #58A30 #58J70 #58J72 #Black Holes and Theoretical Physics #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0910.5946

openalex publication_date 2009/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By developing the Tanaka theory for rank 2 distributions, we completely classify classical Monge equations having maximal finite-dimensional symmetry algebras with fixed (albeit arbitrary) pair of its orders. Investigation of the corresponding Tanaka algebras leads to a new Lie-Backlund theorem. We prove that all flat Monge equations are successive integrable extensions of the Hilbert-Cartan equation. Many new examples are provided.

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