2015/02/23 by La Fuente-Gravy, Laurent
#32Q15 #53C21 #53D20 #53D55 #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1502.06496
We study the Cahen-Gutt moment map on the space of symplectic connections of a symplectic manifold. On a Kähler manifold, we define a Calabi-type functional \mathscrF on the space of Kähler metrics in a given Kähler class. We study the zeroes of \mathscrF. Given a zero of \mathscrF with non-negative Ricci tensor, we show the space of zeroes around the given one has the structure of a finite dimensional embedded submanifold. We give a new motivation, coming from deformation quantisation, for the study of moment maps on infinite dimensional spaces. More precisely, we establish a strong link between trace densities for star products (obtained from Fedosov's type methods) and moment map geometry on infinite dimensional spaces. As a consequence, we provide, on certain Kähler manifolds, a geometric characterization of a space of Fedosov's star products that are closed up to order 3 in ν.