TL;DR
This paper classifies foliations on modular curves induced by holomorphic differentials associated with Hecke eigenforms, showing they are either Strebel or pseudo-Anosov foliations.
Contribution
It establishes a dichotomy for such foliations, identifying their types based on the properties of the underlying eigenforms.
Findings
Foliations are either Strebel or pseudo-Anosov.
Classification depends on the properties of the holomorphic differential.
Provides a clear dichotomy for foliations on modular curves.
Abstract
It is proved, that a foliation on a modular curve given by the vertical trajectories of holomorphic differential corresponding to the Hecke eigenform is either the Strebel foliation or the pseudo-Anosov foliation.
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