Abstract
AbstractA nonlinear flag is a finite sequence of nested closed submanifolds. We study the geometry of Fréchet manifolds of nonlinear flags, in this way generalizing the nonlinear Grassmannians. As an application, we describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms that consist of nested symplectic submanifolds, i.e., symplectic nonlinear flags.
Funder
Austrian Science Fund
Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis
Cited by
4 articles.
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1. Coadjoint orbits of vortex sheets in ideal fluids;Journal of Geometry and Physics;2024-03
2. Weighted nonlinear flag manifolds as coadjoint orbits;Canadian Journal of Mathematics;2023-10-09
3. Pointed vortex loops in ideal 2D fluids;Journal of Physics A: Mathematical and Theoretical;2023-05-23
4. Shape Spaces of Nonlinear Flags;Lecture Notes in Computer Science;2023