Blacker, Casey
Published in
Letters in Mathematical Physics

We extend the Marsden–Weinstein–Meyer symplectic reduction theorem to the setting of multisymplectic manifolds. In this context, we investigate the dependence of the reduced space on the reduction parameters. With respect to a distinguished class of multisymplectic moment maps, an exact stationary phase approximation and nonabelian localization the...

Alonso, Jaume Hohloch, Sonja
Published in
Journal of Nonlinear Science

Semitoric systems are a special class of completely integrable systems with two degrees of freedom that have been symplectically classified by Pelayo and Vũ Ngọc about a decade ago in terms of five symplectic invariants. If a semitoric system has several focus–focus singularities, then some of these invariants have multiple components, one for each...

Haller, Stefan Vizman, Cornelia
Published in
Annals of Global Analysis and Geometry

A 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., symplec...

Das, Pradeep
Published in
Indian Journal of Pure and Applied Mathematics

This paper describes the construction of a natural Hermitian holomorphic line bundle on the stratified moduli space of complex representations of a finite quiver, which are semistable with respect to a fixed rational weight and have a fixed type. It is shown that the curvature of this Hermitian line bundle on each stratum of the moduli space is ess...

KAWASAKI, Morimichi ORITA, Ryuma

(Non-)displaceability of fibers of integrable systems has been an important problem in symplectic geometry. In this paper, for a large class of classical Liouville integrable systems containing the Lagrangian top, the Kovalevskaya top and the C. Neumann problem, we find a non-displaceable fiber for each of them. Moreover, we show that the non-displ...

Cupit-Foutou, Stéphanie Pezzini, Guido Van Steirteghem, Bart
Published in
Selecta Mathematica

We apply the combinatorial theory of spherical varieties to characterize the momentum polytopes of polarized projective spherical varieties. This enables us to derive a classification of these varieties, without specifying the open orbit, as well as a classification of all Fano spherical varieties. In the setting of multiplicity free compact and co...

Diez, Tobias Ratiu, Tudor S.

Given a closed surface endowed with a volume form, we equip the space of compatible Riemannian structures with the structure of an infinite-dimensional symplectic manifold. We show that the natural action of the group of volumepreserving diffeomorphisms by push-forward has a group-valued momentum map that assigns to a Riemannian metric the canonica...

Esen, Oğul Jiménez, Victor M. de León, Manuel Sardón, Cristina
Published in
Regular and Chaotic Dynamics

We discuss, in all generality, the reduction of a Hamilton — Jacobi theory for systems subject to nonholonomic constraints and invariant under the action of a group of symmetries. We consider nonholonomic systems subject to both linear and nonlinear constraints and with different positioning of such constraints with respect to the symmetries.

Arathoon, Philip
Published in
Regular and Chaotic Dynamics

We consider the dynamics and symplectic reduction of the 2-body problem on a sphere of arbitrary dimension. It suffices to consider the case when the sphere is 3-dimensional. As the 3-sphere is a group it acts on itself by left and right multiplication and these together generate the action of the SO(4) symmetry on the sphere. This gives rise to a ...

Bazzoni, Giovanni Goertsches, Oliver
Published in
Forum Mathematicum

We show that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.