Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics
This paper is a natural companion of [Alekseevsky D.V., Alonso Blanco R., Manno G., Pugliese F., Ann. Inst. Fourier (Grenoble) 62 (2012), 497-524, arXiv:1003.5177], generalising its perspectives and results to the context of third-order (2D) Monge-Ampère equations, by using the so-called ''...
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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147730 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics / G. Manno, G. Moreno // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 29 назв. — англ. |
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irk-123456789-1477302019-02-16T01:25:06Z Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics Manno, G. Moreno, G. This paper is a natural companion of [Alekseevsky D.V., Alonso Blanco R., Manno G., Pugliese F., Ann. Inst. Fourier (Grenoble) 62 (2012), 497-524, arXiv:1003.5177], generalising its perspectives and results to the context of third-order (2D) Monge-Ampère equations, by using the so-called ''meta-symplectic structure'' associated with the 8D prolongation M⁽¹⁾ of a 5D contact manifold M. We write down a geometric definition of a third-order Monge-Ampère equation in terms of a (class of) differential two-form on M⁽¹⁾. In particular, the equations corresponding to decomposable forms admit a simple description in terms of certain three-dimensional distributions, which are made from the characteristics of the original equations. We conclude the paper with a study of the intermediate integrals of these special Monge-Ampère equations, herewith called of Goursat type. 2016 Article Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics / G. Manno, G. Moreno // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 29 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D10; 35A30; 58A30; 14M15 DOI:10.3842/SIGMA.2016.032 http://dspace.nbuv.gov.ua/handle/123456789/147730 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 |
This paper is a natural companion of [Alekseevsky D.V., Alonso Blanco R., Manno G., Pugliese F., Ann. Inst. Fourier (Grenoble) 62 (2012), 497-524, arXiv:1003.5177], generalising its perspectives and results to the context of third-order (2D) Monge-Ampère equations, by using the so-called ''meta-symplectic structure'' associated with the 8D prolongation M⁽¹⁾ of a 5D contact manifold M. We write down a geometric definition of a third-order Monge-Ampère equation in terms of a (class of) differential two-form on M⁽¹⁾. In particular, the equations corresponding to decomposable forms admit a simple description in terms of certain three-dimensional distributions, which are made from the characteristics of the original equations. We conclude the paper with a study of the intermediate integrals of these special Monge-Ampère equations, herewith called of Goursat type. |
| format |
Article |
| author |
Manno, G. Moreno, G. |
| spellingShingle |
Manno, G. Moreno, G. Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Manno, G. Moreno, G. |
| author_sort |
Manno, G. |
| title |
Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics |
| title_short |
Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics |
| title_full |
Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics |
| title_fullStr |
Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics |
| title_full_unstemmed |
Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics |
| title_sort |
meta-symplectic geometry of 3rd order monge-ampère equations and their characteristics |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147730 |
| citation_txt |
Meta-Symplectic Geometry of 3rd Order Monge-Ampère Equations and their Characteristics / G. Manno, G. Moreno // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 29 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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