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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| Дата: | 2015 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147123 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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 |
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irk-123456789-1471232019-02-14T01:24:32Z Constructing Involutive Tableaux with Guillemin Normal Form Smith, A.D. 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. 2015 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147123 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Smith, A.D. |
| spellingShingle |
Smith, A.D. Constructing Involutive Tableaux with Guillemin Normal Form Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Smith, A.D. |
| author_sort |
Smith, A.D. |
| title |
Constructing Involutive Tableaux with Guillemin Normal Form |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT smithad constructinginvolutivetableauxwithguilleminnormalform |
| first_indexed |
2023-05-20T17:26:38Z |
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2023-05-20T17:26:38Z |
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