The geometry of $\mathbb {C}^2$ equipped with Warren’s metric
Volume 121 / 2018
Annales Polonici Mathematici 121 (2018), 243-249
MSC: Primary 32Q15.
DOI: 10.4064/ap180618-28-8
Published online: 12 October 2018
Abstract
The aim of this note is to describe the geometry of $\mathbb {C}^2$ equipped with a Kähler metric defined by Warren. It is shown that with that metric $\mathbb {C}^2$ is a flat manifold. Explicit formulae for geodesics and the volume of the geodesic ball are also computed. Finally, a family of similar flat metrics is constructed.
