2017/08/04 by Abdellah Lahdili, Lahdili, Abdellah
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1708.01507
openalex publication_date 2017/08/04 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We obtain a structure theorem for the group of holomorphic automorphisms of a\nconformally K "ahler, Einstein-Maxwell metric, extending the classical results\nof Matsushima, Licherowicz and Calabi in the K "ahler-Einstein, cscK, and\nextremal K "ahler cases. Combined with previous results of LeBrun,\nApostolov-Maschler and Futaki-Ono, this completes the classification of the\nconformally K "ahler, Einstein--Maxwell metrics on mathbbCP1 \×\n mathbbCP1. We also use our result in order to introduce a (relative)\nMabuchi energy in the more general context of (K, q, a)-extremal K "ahler\nmetrics in a given K "ahler class, and show that the existence of (K, q,\na)-extremal K "ahler metrics is stable under small deformation of the K "ahler\nclass, the Killing vector field K and the normalization constant a.\n