Totally geodesic subgroups of diffeomorphisms

DOI10.1016/S0393-0440(01)00096-1zbMath1004.58004arXivmath/0103220OpenAlexW3105467097MaRDI QIDQ1603287

Cornelia Vizman, Stefan Haller, Josef Teichmann

Publication date: 11 July 2002

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0103220

zbMATH Keywords

volume preserving diffeomorphismsHamiltonian diffeomorphismssymplectic diffeomorphismsgeodesic equation on infinite Lie groupgroup of diffeomorphisms as a manifold

Mathematics Subject Classification ID

Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65)

Related Items

Möbius fluid dynamics on the unitary groups, Geometric investigations of a vorticity model equation, Central extensions of semidirect products and geodesic equations, Coadjoint orbits of vortex sheets in ideal fluids, The geometry of axisymmetric ideal fluid flows with swirl, On Euler-Arnold equations and totally geodesic subgroups, Cocycles and stream functions in quasigeostrophic motion

Cites Work

• Topological methods in hydrodynamics
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• The splitting theorem for manifolds of nonnegative Ricci curvature
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