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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147123 |
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| Cite this: | 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| _version_ | 1862664218089619456 |
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| author | Smith, A.D. |
| author_facet | Smith, A.D. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T15:13:51Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147123 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:13:51Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Constructing Involutive Tableaux with Guillemin Normal Form Smith, A.D. |
| title | 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_short | Constructing Involutive Tableaux with Guillemin Normal Form |
| title_sort | constructing involutive tableaux with guillemin normal form |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147123 |
| work_keys_str_mv | AT smithad constructinginvolutivetableauxwithguilleminnormalform |