Geodesic Equations on Diffeomorphism Groups

2008/03/11 by Cornelia Vizman
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geophysics and Gravity Measurements #Nonlinear Waves and Solitons #math.DG

paper · pdf · doi:10.3842/sigma.2008.030

published as SIGMA 4 (2008), 030, 22 pages · This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

arxiv created 2008/03/11 · openalex publication_date 2008/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Geodesics and curvature of semidirect product groups
• On the stability of periodic 2D Euler-alpha flows
• Extensions of (super) Lie algebras
• Abelian extensions of infinite-dimensional Lie groups
• Momentum Maps and Measure-valued Solutions (Peakons, Filaments and Sheets) for the EPDiff Equation