Some QCH Kähler surfaces with zero scalar curvature
Volume 133 / 2024
Annales Polonici Mathematici 133 (2024), 271-285
MSC: Primary 53C55; Secondary 53C25, 53B35
DOI: 10.4064/ap240131-10-2
Published online: 22 February 2025
Abstract
We prove that some well-known Kähler surfaces with zero scalar curvature are QCH Kähler. We prove that the family of generalized Taub-NUT Kähler surfaces parameterized by $k\in [-1,1]$ is of orthotoric type for $k\in (-1,1)$ and of Calabi type for $k\in \{-1,1\}$ and the Burns metric is of Calabi type.
