The geometry of $\mathbb{C}^2$ equipped with Warren's metric

Szymon Myga

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arXiv · 1706.07769

The geometry of $\mathbb{C}^2$ equipped with Warren's metric

Szymon Myga

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Abstract

The aim of this note is to describe the geometry of $\mathbb{C}^2$ equipped with a K\"{a}hler metric defined by Warren. It is shown that with that metric $\mathbb{C}^2$ 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.

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Szymon Myga. 2017-06-23. The geometry of $\mathbb{C}^2$ equipped with Warren's metric. https://arxiv.org/abs/1706.07769

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