2017/09/30 by Abdellah Lahdili, Lahdili, Abdellah
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1710.00235
openalex publication_date 2017/09/30 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28
We prove that if a compact smooth polarized complex manifold admits in the corresponding Hodge Kähler class a conformally Kähler, Einstein--Maxwell metric, or more generally, a Kähler metric of constant (ξ, a, p)-scalar curvature, then this metric minimizes the (ξ,a,p)-Mabuchi functional. Our method of proof extends the approach introduced by Donaldson and developed by Li and Sano--Tipler, via finite dimensional approximations and generalized balanced metrics. As an application of our result and the recent construction of Koca--Tønnesen-Friedman, we describe the Kähler classes on a geometrically ruled complex surface of genus greater than 2, which admit conformally Kähler, Einstein-Maxwell metrics.