Ergodic Geodesic Flows and First Kind Flute Surfaces
Geometric Topology
2026-01-30 v2
Abstract
We study flute surfaces and extend results of Pandazis and \v{S}ari\'c giving necessary and sufficient conditions on the Fenchel-Nielsen coordinates of the surface to be of the first kind. As a consequence of the first result, we characterize parabolic flute surfaces (i.e. flute surfaces with ergodic geodesic flow) with twist parameters in {0,1/2}, extending the work of Pandazis and \v{S}ari\'c.
Keywords
Cite
@article{arxiv.2510.24576,
title = {Ergodic Geodesic Flows and First Kind Flute Surfaces},
author = {Erick Gordillo Herrerías and Nolwenn Le Quellec},
journal= {arXiv preprint arXiv:2510.24576},
year = {2026}
}
Comments
36 pages, 23 figures. 1 Appendix