Constructing Involutive Tableaux with Guillemin Normal Form

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 pro...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2015
1. Verfasser: Smith, A.D.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2015
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/147123
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Constructing Involutive Tableaux with Guillemin Normal Form / A.D. Smith // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 9 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147123
record_format dspace
spelling Smith, A.D.
2019-02-13T17:02:07Z
2019-02-13T17:02:07Z
2015
Constructing Involutive Tableaux with Guillemin Normal Form / A.D. Smith // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 9 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 58A15; 58H10
DOI:10.3842/SIGMA.2015.053
https://nasplib.isofts.kiev.ua/handle/123456789/147123
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.
Thanks to Deane Yang for several helpful conversations. Thanks also to the anonymous referees, whose suggestions improved the style and focus of this article significantly.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Constructing Involutive Tableaux with Guillemin Normal Form
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Constructing Involutive Tableaux with Guillemin Normal Form
spellingShingle Constructing Involutive Tableaux with Guillemin Normal Form
Smith, A.D.
title_short Constructing Involutive Tableaux with Guillemin Normal Form
title_full Constructing Involutive Tableaux with Guillemin Normal Form
title_fullStr Constructing Involutive Tableaux with Guillemin Normal Form
title_full_unstemmed Constructing Involutive Tableaux with Guillemin Normal Form
title_sort constructing involutive tableaux with guillemin normal form
author Smith, A.D.
author_facet Smith, A.D.
publishDate 2015
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description 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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147123
citation_txt Constructing Involutive Tableaux with Guillemin Normal Form / A.D. Smith // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 9 назв. — англ.
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