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: Vizman, C.
Format: Article
Language:English
Published: Інститут математики НАН України 2008
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
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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.
first_indexed 2025-12-07T19:45:07Z
format Article
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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