Existence of Generalized Maxwell–Einstein Metrics on Completions of Certain Line Bundles

Jing Chen and Daniel Guan ()
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Jing Chen: School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
Daniel Guan: School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

Mathematics, 2025, vol. 13, issue 20, 1-51

Abstract: In Kähler geometry, Calabi extremal metrics serves as a class of more available special metrics than Kähler metrics with constant scalar curvatures, as a generalization of Kähler Einstein metrics. In recent years, Maxwell–Einstein metrics (or conformally Kähler Einstein–Maxwell metrics) appeared as another alternative choice for Calabi extremal metrics. It turns out that some similar metrics defined by Futaki and Ono have similar roles in the Kähler geometry. In this paper, we prove that for some completions of certain line bundles, there is at least one k -generalized Maxwell–Einstein metric defined by Futaki and Ono conformally related to a metric in any given Kähler class for any integer 3 ≤ k ≤ 13 .

Keywords: Hermitian metrics; generalized Maxwell–Einstein metrics; complex manifolds; scalar curvature; fiber bundle; almost homogeneous manifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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