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Полная версия
ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2015, том 11, 053, 14 стр. (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

Аннотация: 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.

Ключевые слова: involutivity; tableau; symbol; exterior differential systems.

MSC: 58A15; 58H10

Поступила: 15 декабря 2014 г.; в окончательном варианте 1 июля 2015 г.; опубликована 9 июля 2015 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2015.053



Реферативные базы данных:
ArXiv: 1410.7593


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