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Some QCH Kahler surfaces with zero scalar curvature

Differential Geometry 2025-02-11 v2

Abstract

In this paper we prove that some well known K\"ahler surfaces with zero scalar curvature are QCH K\"ahler. We prove that family of generalized Taub-Nut K\"ahler surfaces parametrized by k[1,1]k\in[-1,1] is of orthotoric type for k(1,1)k\in(-1,1) and of Calabi type for k{1,1}k\in\{-1,1\} and the Burn's metric is of Calabi type.

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Cite

@article{arxiv.2207.13468,
  title  = {Some QCH Kahler surfaces with zero scalar curvature},
  author = {Włodzimierz Jelonek},
  journal= {arXiv preprint arXiv:2207.13468},
  year   = {2025}
}

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9 pages