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

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

2009-10-30

arxiv.org/abs/0910.5946v1

Mathematics

Differential Geometry

35 pages

Scientific paper

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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