Geodesic Equations on Diffeomorphism Groups
We bring together those systems of hydrodynamical type that can be written as geodesic equations on diffeomorphism groups or on extensions of diffeomorphism groups with right invariant L² or H¹ metrics. We present their formal derivation starting from Euler's equation, the first order equation...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2008 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149033 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Geodesic Equations on Diffeomorphism Groups / C. Vizman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 63 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734737148215296 |
|---|---|
| author | Vizman, C. |
| author_facet | Vizman, C. |
| citation_txt | Geodesic Equations on Diffeomorphism Groups / C. Vizman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 63 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We bring together those systems of hydrodynamical type that can be written as geodesic equations on diffeomorphism groups or on extensions of diffeomorphism groups with right invariant L² or H¹ metrics. We present their formal derivation starting from Euler's equation, the first order equation satisfied by the right logarithmic derivative of a geodesic in Lie groups with right invariant metrics.
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| first_indexed | 2025-12-07T19:45:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149033 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:45:07Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Vizman, C. 2019-02-19T13:10:41Z 2019-02-19T13:10:41Z 2008 Geodesic Equations on Diffeomorphism Groups / C. Vizman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 63 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 58D05; 35Q35 https://nasplib.isofts.kiev.ua/handle/123456789/149033 We bring together those systems of hydrodynamical type that can be written as geodesic equations on diffeomorphism groups or on extensions of diffeomorphism groups with right invariant L² or H¹ metrics. We present their formal derivation starting from Euler's equation, the first order equation satisfied by the right logarithmic derivative of a geodesic in Lie groups with right invariant metrics. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). This work was done with the financial support of Romanian Ministery of Education and Research under the grant CNCSIS 95GR/2007. I acknowledge the support from the ICTP Of fice of External Activities for attending the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” in Kyiv. I am most grateful to Tudor Ratiu and Francois Gay-Balmaz for their preprints and for very good suggestions, and to the referees for their very substantial and constructive comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geodesic Equations on Diffeomorphism Groups Article published earlier |
| spellingShingle | Geodesic Equations on Diffeomorphism Groups Vizman, C. |
| title | Geodesic Equations on Diffeomorphism Groups |
| title_full | Geodesic Equations on Diffeomorphism Groups |
| title_fullStr | Geodesic Equations on Diffeomorphism Groups |
| title_full_unstemmed | Geodesic Equations on Diffeomorphism Groups |
| title_short | Geodesic Equations on Diffeomorphism Groups |
| title_sort | geodesic equations on diffeomorphism groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149033 |
| work_keys_str_mv | AT vizmanc geodesicequationsondiffeomorphismgroups |