Geodesics on the symplectomorphism group

DOI10.1007/s00039-012-0150-2zbMath1252.58006OpenAlexW2008825516MaRDI QIDQ412035

David G. Ebin

Publication date: 3 May 2012

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00039-012-0150-2

zbMATH Keywords

spraydiffeomorphismHodge decompositionHilbert manifoldgeodesicalmost complex structurePicard iterationglobal existence of solutionssymplectic manifoldNoether's theoremsubmersionsymplectomorphismweak Riemannian metric

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Geodesics in global differential geometry (53C22) Global theory of symplectic and contact manifolds (53D35) Geodesic flows in symplectic geometry and contact geometry (53D25) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Differentiability questions for infinite-dimensional manifolds (58B10)

Related Items (13)

On completeness of groups of diffeomorphisms ⋮ Groups of Diffeomorphisms and Fluid Motion: Reprise ⋮ Möbius fluid dynamics on the unitary groups ⋮ The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms ⋮ The \(L^p\)-diameter of the group of area-preserving diffeomorphisms of \(S^2\) ⋮ Dynamics of symplectic fluids and point vortices ⋮ Lagrange multiplier functionals and their applications in symplectic geometry and string topology ⋮ On a linear problem arising in dynamic boundaries ⋮ Conjugate points on the symplectomorphism group ⋮ The coadjoint operator, conjugate points, and the stability of ideal fluids ⋮ Sobolev \(H^1\) geometry of the symplectomorphism group ⋮ Fredholm properties of the \(L^2\) exponential map on the symplectomorphism group ⋮ Riemannian geometry of the contactomorphism group

Cites Work

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• On classical solutions of the two-dimensional non-stationary Euler equation
• Groups of diffeomorphisms and the motion of an incompressible fluid
• A Concise Presentation of the Euler Equations of Hydrodynamics
• On the Volume Elements on a Manifold
• On the space of Riemannian metrics

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