English

Conformally K\"ahler, Einstein-Maxwell metrics on Hirzebruch surfaces

Differential Geometry 2021-01-08 v2

Abstract

In this note we prove that a special family of Killing potentials on certain Hirzebruch complex surfaces, found by Futaki and Ono, gives rise to new conformally K\"ahler, Einstein-Maxwell metrics. The correspondent K\"ahler metrics are ambitoric but they are not given by the Calabi ansatz. This answers in positive questions raised by Futaki-Ono.

Keywords

Cite

@article{arxiv.2001.11541,
  title  = {Conformally K\"ahler, Einstein-Maxwell metrics on Hirzebruch surfaces},
  author = {Isaque Viza de Souza},
  journal= {arXiv preprint arXiv:2001.11541},
  year   = {2021}
}

Comments

22 pages, updated references, corrected typos, revised and expanded section 6, results unchanged. Comments are welcome

R2 v1 2026-06-23T13:25:44.536Z