Weighted nonlinear flag manifolds as coadjoint orbits
Differential Geometry
2024-11-20 v1 Symplectic Geometry
Abstract
A weighted nonlinear flag is a nested set of closed submanifolds, each submanifold endowed with a volume density. We study the geometry of Frechet manifolds of weighted nonlinear flags, in this way generalizing the weighted nonlinear Grassmannians. When the ambient manifold is symplectic, we use these nonlinear flags to describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms, orbits that consist of weighted isotropic nonlinear flags.
Cite
@article{arxiv.2301.00428,
title = {Weighted nonlinear flag manifolds as coadjoint orbits},
author = {Stefan Haller and Cornelia Vizman},
journal= {arXiv preprint arXiv:2301.00428},
year = {2024}
}