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October 15, 2025Open Access

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

Key Points

At least one k-generalized maxwell-einstein metric exists on some completions of line bundles, offering new insights.
The proof confirms the relationship between these metrics and existing kaähler class metrics outlined by futaki and ono.
The focus spans integer values from 3 to 13 for the k-generalization, emphasizing the metrics' versatility in geometry.
The study furthers the understanding of calabi extremal metrics and their significance in geometrical structures.

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.

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