Weighted nonlinear flag manifolds as coadjoint orbits

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.

References in corpus (2)

• Geometric Structures on Spaces of Weighted Submanifolds
• Pointed vortex loops in ideal 2D fluids

Cited by in corpus (3)

• A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting
• A dual pair for the group of volume preserving diffeomorphisms
• Manifolds of vortex loops as coadjoint orbits