32 citations · 183 across the 32 of their papers we have counts for
39 papers
Generalized Marsden-Weinstein symplectic structures
Boris Khesin, Klas Modin, Cornelia Vizman
We define a symplectic structure on singular 1-form densities and a presymplectic structure on augmented triples, a compressible analog of the Marsden--Weinstein symplectic structu…
Universal central extension of the Lie algebra of exact divergence-free vector fields
Bas Janssens, Leonid Ryvkin, Cornelia Vizman
We construct the universal central extension of the Lie algebra of exact divergence-free vector fields, proving a conjecture by Claude Roger from 1995. The proof relies on the anal…
A dual pair for the group of volume preserving diffeomorphisms
Stefan Haller, Cornelia Vizman
We use cotangent bundles of spaces of smooth embeddings to construct symplectic dual pairs involving the group of volume preserving diffeomorphisms. Via symplectic reduction we obt…
Generalized double bracket vector fields
Petre Birtea, Zohreh Ravanpak, Cornelia Vizman
We generalize double bracket vector fields, originally defined on semisimple Lie algebras, to Poisson manifolds equipped with a pseudo-Riemannian metric by utilizing a symmetric co…
Shape spaces of nonlinear flags
Ioana Ciuclea, Alice Barbara Tumpach, Cornelia Vizman
The gauge invariant elastic metric on the shape space of surfaces involves the mean curvature and the normal deformation, i.e. the sum and the difference of the principal curvature…
Weighted nonlinear flag manifolds as coadjoint orbits
Stefan Haller, Cornelia Vizman
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 f…