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arXiv · 1410.7593

Constructing Involutive Tableaux with Guillemin Normal Form

Abraham D. Smith
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Abstract

Involutivity is the algebraic property that guarantees solutions to an analytic and torsion-free exterior differential system or partial differential equation via the Cartan-K\"ahler theorem. Guillemin normal form establishes that the prolonged symbol of an involutive system admits a commutativity property on certain subspaces of the prolonged tableau. This article examines Guillemin normal form in detail, aiming at a more systematic approach to classifying involutive systems. The main result is an explicit quadratic condition for involutivity of the type suggested but not completed in Chapter IV, \S 5 of the book Exterior Differential Systems by Bryant, Chern, Gardner, Goldschmidt, and Griffiths. This condition enhances Guillemin normal form and characterizes involutive tableaux.

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Abraham D. Smith. 2014-10-28. Constructing Involutive Tableaux with Guillemin Normal Form. https://doi.org/10.3842/sigma.2015.053

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