We set S1 = R/2πZ throughout. Let (M,ω) be a symplectic manifold. A symplectic S1-action on (M,ω) is a smooth family ψt ∈ Symp(M,ω), t ∈ S1, such that ψt+s = ψt ◦ ψs for any t, s ∈ S1. One can easily check that the corresponding vector fields Xt ≡ d dtψt ◦ψ −1 t is time-independent, i.e., Xt = X is constant in t. We call X the associated vector field of the given symplectic S1-action. Note that...

In this paper a new character description method, based on the combination of structural and statistical approaches, is presented. Characters are preliminarily decomposed in terms of structural primitives (circular arcs) and successively described in terms of statistical features (geometric moments). The obtained description is much more stable and yields significant improvements in classificat...

This paper gives an essentially self-contained exposition (except for appeal to the Lojasiewicz gradient inequality) of geometric invariant theory from a differential viewpoint. Central ingredients are moment-weight inequality (relating Mumford numerical invariants norm moment map), negative flow map squared, and Kempf-Ness function.

In this paper we reopen the discussion of gauging the two-dimensional off-shell (2, 2) supersymmetric sigma models written in terms of semichiral superfields. The associated target space geometry of this particular sigma model is generalized Kähler (or bi-hermitean with two noncommuting complex structures). The gauging of the isometries of the sigma model is now done by coupling the semichiral ...

We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian quasi-Poisson manifolds fit into this framework by constructing an “inversion” procedure relating quasi-Poisson bivectors to twisted Dirac structures. Dedicated to Al...

Given a Riemannian manifold together with a group of isometries, we discuss MCF of the orbits and some applications: eg, finding minimal orbits. We then specialize to Lagrangian orbits in Kaehler manifolds. In particular, in the Kaehler-Einstein case we find a relation between MCF and moment maps which, for example, proves that the minimal Lagrangian orbits are isolated.