The geometry of $\mathbb{C}^2$ equipped with Warren's metric
Differential Geometry
2018-08-28 v2
Abstract
The aim of this note is to describe the geometry of equipped with a K\"{a}hler metric defined by Warren. It is shown that with that metric is a flat manifold. Explicit formulae for geodesics and volume of geodesic ball are also computed. Finally, a family of similar flat metrics is constructed.
Cite
@article{arxiv.1706.07769,
title = {The geometry of $\mathbb{C}^2$ equipped with Warren's metric},
author = {Szymon Myga},
journal= {arXiv preprint arXiv:1706.07769},
year = {2018}
}
Comments
Final version to appear in Annales Polonici Mathematici