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Symmetry, Integrability and Geometry: Methods and Applications, 2008, Volume 4, 030, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2008.030 (Mi sigma283) 		 
This article is cited in 25 scientific papers (total in 25 papers)

Geodesic Equations on Diffeomorphism Groups

Cornelia Vizman

Department of Mathematics, West University of Timişoara, Romania
Full-text PDF (365 kB) Citations (25)
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DOI: https://doi.org/10.3842/SIGMA.2008.030
Abstract: 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 $L^2$ or $H^1$ 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.
Keywords: Euler's equation; diffeomorphism group; group extension; geodesic equation.
Received: November 13, 2007; in final form March 1, 2008; Published online March 11, 2008
Bibliographic databases:
Document Type: Article
MSC: 58D05; 35Q35
Language: English
Citation: Cornelia Vizman, “Geodesic Equations on Diffeomorphism Groups”, SIGMA, 4 (2008), 030, 22 pp.
Citation in format AMSBIB
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\by Cornelia Vizman
\paper Geodesic Equations on Diffeomorphism Groups
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    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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