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Mathematics
Volume 13
Issue 20
10.3390/math13203264
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Article

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

by
Jing Chen
1,2 and
Daniel Guan
1,3,*
1
School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
2
School of Mathematics and Statistics, Henan Normal University, Xinxiang 453007, China
3
Department of Mathematics, The University of California at Riverside, Riverside, CA 92521, USA
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(20), 3264; https://doi.org/10.3390/math13203264 (registering DOI)
Submission received: 25 August 2025 / Revised: 2 October 2025 / Accepted: 6 October 2025 / Published: 12 October 2025
Versions Notes

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 Hermitian metrics; generalized Maxwell–Einstein metrics; complex manifolds; scalar curvature; fiber bundle; almost homogeneous manifolds

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MDPI and ACS Style

Chen, J.; Guan, D. Existence of Generalized Maxwell–Einstein Metrics on Completions of Certain Line Bundles. Mathematics 2025, 13, 3264. https://doi.org/10.3390/math13203264

AMA Style

Chen J, Guan D. Existence of Generalized Maxwell–Einstein Metrics on Completions of Certain Line Bundles. Mathematics. 2025; 13(20):3264. https://doi.org/10.3390/math13203264

Chicago/Turabian Style

Chen, Jing, and Daniel Guan. 2025. "Existence of Generalized Maxwell–Einstein Metrics on Completions of Certain Line Bundles" Mathematics 13, no. 20: 3264. https://doi.org/10.3390/math13203264

APA Style

Chen, J., & Guan, D. (2025). Existence of Generalized Maxwell–Einstein Metrics on Completions of Certain Line Bundles. Mathematics, 13(20), 3264. https://doi.org/10.3390/math13203264

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