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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 053, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.053
(Mi sigma1034)
 

Constructing Involutive Tableaux with Guillemin Normal Form

Abraham D. Smith

Department of Mathematics, Statistics and Computer Science, University of Wisconsin-Stout, Menomonie, WI 54751-2506, USA
References:
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–Kähler 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, § 5 of the book Exterior Differential Systems by Bryant, Chern, Gardner, Goldschmidt, and Griffiths. This condition enhances Guillemin normal form and characterizes involutive tableaux.
Keywords: involutivity; tableau; symbol; exterior differential systems.
Received: December 15, 2014; in final form July 1, 2015; Published online July 9, 2015
Bibliographic databases:
Document Type: Article
MSC: 58A15; 58H10
Language: English
Citation: Abraham D. Smith, “Constructing Involutive Tableaux with Guillemin Normal Form”, SIGMA, 11 (2015), 053, 14 pp.
Citation in format AMSBIB
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