Ergodic Geodesic Flows and First Kind Flute Surfaces
Abstract
We study flute surfaces and extend results of Pandazis and Sari\'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 Sari\'c.
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