Geodesic Equations on Diffeomorphism Groups

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• ISSN: 1815-0659
• Main Author: Vizman, C.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149033
• 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.

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...