2016/12/09 by Laurent La Fuente-Gravy, La Fuente-Gravy, Laurent
Mathematics · #32Q15 #53C21 #53D20 #53D55 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1612.02946
openalex publication_date 2016/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study obstructions to the existence of closed Fedosov's star products on a given Kähler manifold. In our previous paper, we proved that the Levi-Civita connection of a Kähler manifold will produce a closed (in the sense of Connes-Flato-Sternheimer) Fedosov's star product only if it is a zero of the Cahen-Gutt moment map on the space of symplectic connections. By analogy with the Futaki invariant obstructing the existence of cscK metrics, we build an obstruction for the existence of zero of the moment map and hence for the existence of closed Fedosov's star products on a Kähler manifold.