Monge-Ampère Systems with Lagrangian Pairs
The classes of Monge-Ampère systems, decomposable and bi-decomposable Monge-Ampère systems, including equations for improper affine spheres and hypersurfaces of constant Gauss-Kronecker curvature are introduced. They are studied by the clear geometric setting of Lagrangian contact structures, based...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2015 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2015
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147154 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Monge-Ampère Systems with Lagrangian Pairs / G. Ishikawa, Y. Machida // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 31 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707536882302976 |
|---|---|
| author | Ishikawa, G. Machida, Y. |
| author_facet | Ishikawa, G. Machida, Y. |
| citation_txt | Monge-Ampère Systems with Lagrangian Pairs / G. Ishikawa, Y. Machida // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 31 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The classes of Monge-Ampère systems, decomposable and bi-decomposable Monge-Ampère systems, including equations for improper affine spheres and hypersurfaces of constant Gauss-Kronecker curvature are introduced. They are studied by the clear geometric setting of Lagrangian contact structures, based on the existence of Lagrangian pairs in contact structures. We show that the Lagrangian pair is uniquely determined by such a bi-decomposable system up to the order, if the number of independent variables ≥3. We remark that, in the case of three variables, each bi-decomposable system is generated by a non-degenerate three-form in the sense of Hitchin. It is shown that several classes of homogeneous Monge-Ampère systems with Lagrangian pairs arise naturally in various geometries. Moreover we establish the upper bounds on the symmetry dimensions of decomposable and bi-decomposable Monge-Ampère systems respectively in terms of the geometric structure and we show that these estimates are sharp (Proposition 4.2 and Theorem 5.3).
|
| first_indexed | 2025-12-07T17:06:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147154 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:06:09Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ishikawa, G. Machida, Y. 2019-02-13T17:48:28Z 2019-02-13T17:48:28Z 2015 Monge-Ampère Systems with Lagrangian Pairs / G. Ishikawa, Y. Machida // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 31 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58K20; 53A15; 53C42 DOI:10.3842/SIGMA.2015.081 https://nasplib.isofts.kiev.ua/handle/123456789/147154 The classes of Monge-Ampère systems, decomposable and bi-decomposable Monge-Ampère systems, including equations for improper affine spheres and hypersurfaces of constant Gauss-Kronecker curvature are introduced. They are studied by the clear geometric setting of Lagrangian contact structures, based on the existence of Lagrangian pairs in contact structures. We show that the Lagrangian pair is uniquely determined by such a bi-decomposable system up to the order, if the number of independent variables ≥3. We remark that, in the case of three variables, each bi-decomposable system is generated by a non-degenerate three-form in the sense of Hitchin. It is shown that several classes of homogeneous Monge-Ampère systems with Lagrangian pairs arise naturally in various geometries. Moreover we establish the upper bounds on the symmetry dimensions of decomposable and bi-decomposable Monge-Ampère systems respectively in terms of the geometric structure and we show that these estimates are sharp (Proposition 4.2 and Theorem 5.3). The first author was partially supported by Grants-in-Aid for Scientific Research No. 19654006.
 The second author was partially supported by Grants-in-Aid for Scientific Research (C)
 No. 18540105. The authors would like to thank anonymous referees for the valuable comments
 to improve the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Monge-Ampère Systems with Lagrangian Pairs Article published earlier |
| spellingShingle | Monge-Ampère Systems with Lagrangian Pairs Ishikawa, G. Machida, Y. |
| title | Monge-Ampère Systems with Lagrangian Pairs |
| title_full | Monge-Ampère Systems with Lagrangian Pairs |
| title_fullStr | Monge-Ampère Systems with Lagrangian Pairs |
| title_full_unstemmed | Monge-Ampère Systems with Lagrangian Pairs |
| title_short | Monge-Ampère Systems with Lagrangian Pairs |
| title_sort | monge-ampère systems with lagrangian pairs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147154 |
| work_keys_str_mv | AT ishikawag mongeamperesystemswithlagrangianpairs AT machiday mongeamperesystemswithlagrangianpairs |