2024/05/09 by Yasuhiro Nakagawa, Satoshi Nakamura, Nakagawa, Yasuhiro +1 · 1 citation
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2405.05604
Motivated by the notion of multiplier Hermitian-Einstein metric of type σ introduced by Mabuchi, we introduce the notion of σ-extremal Kähler metrics on compact Kähler manifolds, which generalizes Calabi's extremal Kähler metrics. We characterize the existence of this metric in terms of the coercivity of a certain functional on the space of Kähler metrics to show that, on a Fano manifold, the existence of a multiplier Hermitian-Einstein metric of type σ implies the existence of a σ-extremal Kähler metric.