32 citations · 183 across the 32 of their papers we have counts for
21 papers · 1 filter
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…
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…
Induced differential characters on nonlinear Graßmannians
Tobias Diez, Bas Janssens, Karl-Hermann Neeb +1
Using a nonlinear version of the tautological bundle over Graßmannians, we construct a transgression map for differential characters from to the nonlinear Graßmannians $\mathrm…
Nonlinear flag manifolds as coadjoint orbits
Stefan Haller, Cornelia Vizman
A nonlinear flag is a finite sequence of nested closed submanifolds. We study the geometry of Frechet manifolds of nonlinear flags, in this way generalizing the nonlinear Grassmann…