Finsler metrics on $1/n$-translation structures on surfaces

Beatrice Pozzetti; Jiajun Shi

Finsler metrics on $1/n$-translation structures on surfaces

Geometric Topology 2026-04-03 v1 Differential Geometry

Authors: Beatrice Pozzetti , Jiajun Shi

Abstract

We define compatible Finsler distances on $1/n$ -translation surfaces, we study their geodesics, and construct a Liouville current for each such metric, that is a geodesic current that encodes the information of the length of the closed curves. The construction is based on multi-foliations, a generalization of measured foliations of independent interest.

Keywords

finsler geometry

Cite

@article{arxiv.2604.02243,
  title  = {Finsler metrics on $1/n$-translation structures on surfaces},
  author = {Beatrice Pozzetti and Jiajun Shi},
  journal= {arXiv preprint arXiv:2604.02243},
  year   = {2026}
}

Comments

34 pages, 18 figures

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