2018/02/28 by Akito Futaki, Futaki, Akito, Hajime Ono +1
Mathematics · Physics and Astronomy · #32Q15 #46L65 #53C55 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1802.10292
openalex publication_date 2018/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that if a compact Kaehler manifold M of non-negative Ricci curvature admits closed Fedosov star product then the reduced Lie algebra of holomorphic vector fields on M is reductive. This comes in pair with the obstruction previously found by La Fuente-Gravy. More generally we consider the squared norm of Cahen-Gutt moment map as in the same spirit of Calabi functional for the scalar curvature in cscK problem, and prove a Cahen-Gutt version of Calabi's theorem on the structure of the Lie algebra of holomorphic vector fields for extremal Kaehler manifolds. The proof uses a Hessian formula for the squared norm of Cahen-Gutt moment map.