Geodesic curves on Shimura surfaces

Abstract

We parametrize the commensurability classes of curves on Shimura surfaces that are totally geodesic, i.e., the commensurability classes of so-called $\mathbb{C}$-Fuchsian subgroups. In particular, if a Shimura surface contains one commensurability class of totally geodesic curves, it contains infinitely many.

This is broken off from our previous work arxiv:1105.1154

References in corpus (3)

• Spectre automorphe des variétés hyperboliques et applications topologiques
• On the equidistribution of totally geodesic submanifolds in compact locally symmetric spaces and application to boundedness results for negative curves and exceptional divisors
• A classification of $\mathbb{R}$-Fuchsian subgroups of Picard modular groups

Cited by in corpus (1)

• A classification of $\mathbb{R}$-Fuchsian subgroups of Picard modular groups