Ergodic Geodesic Flows and First Kind Flute Surfaces

Erick Gordillo Herrerías; Nolwenn Le Quellec

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arXiv · 2510.24576

Ergodic Geodesic Flows and First Kind Flute Surfaces

Erick Gordillo Herrerías·Nolwenn Le Quellec

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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.

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Erick Gordillo Herrerías, Nolwenn Le Quellec. 2025-10-28. Ergodic Geodesic Flows and First Kind Flute Surfaces. https://arxiv.org/abs/2510.24576

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