Conjugacies of geodesic flows in affine cylinders and tori

Xavier Buff; Guillaume Tahar

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arXiv · 2509.06391

Conjugacies of geodesic flows in affine cylinders and tori

Xavier Buff·Guillaume Tahar

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Abstract

Affine cylinders (genus zero surfaces with two singularities) and affine tori (genus one surfaces without singularities) are among the simplest examples of surfaces endowed with a complex affine structure. Their geodesic flows are particularly tractable. In this article, we provide explicit necessary and sufficient conditions under which the geodesic flows on such surfaces are conjugate, in the topological and in the holomorphic category.

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Xavier Buff, Guillaume Tahar. 2025-09-08. Conjugacies of geodesic flows in affine cylinders and tori. https://arxiv.org/abs/2509.06391

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