Principal bundles of embeddings and nonlinear Grassmannians

DOI10.1007/s10455-014-9424-2zbMath1318.46061arXiv1402.1512OpenAlexW1987912130MaRDI QIDQ465482

François Gay-Balmaz, Cornelia Vizman

Publication date: 31 October 2014

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.1512

zbMATH Keywords

nonlinear GrassmannianFréchet manifoldmanifolds of embeddings

Mathematics Subject Classification ID

Spaces of embeddings and immersions (58D10) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Manifolds of mappings (58D15) Infinite-dimensional manifolds (46T05)

Related Items (6)

Remarks on the space of volume preserving embeddings ⋮ Hyperspaces of smooth convex bodies up to congruence ⋮ Riemannian geometry of the space of volume preserving immersions ⋮ Coadjoint orbits of vortex sheets in ideal fluids ⋮ Nonlinear flag manifolds as coadjoint orbits ⋮ Manifolds of Mappings for Continuum Mechanics

Cites Work

• On the geometry and quantization of symplectic Howe pairs
• Reduced variational formulations in free boundary continuum mechanics
• Lie group structures on groups of smooth and holomorphic maps on non-compact manifolds
• The Hamiltonian structure for dynamic free boundary problems
• Nonlinear Grassmannians as coadjoint orbits
• Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups
• Remarks on the space of volume preserving embeddings
• Implicit functions from topological vector spaces to Banach spaces
• Groups of diffeomorphisms and the motion of an incompressible fluid
• A dual pair for free boundary fluids
• The inverse function theorem of Nash and Moser
• Differential Topology
• Riemannian geometry
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