Some arithmetic aspects of ortho-integral surfaces
Abstract
We investigate ortho-integral (OI) hyperbolic surfaces with totally geodesic boundaries, defined by the property that every orthogeodesic (i.e., a geodesic arc meeting the boundary perpendicularly at both endpoints) has an integer cosh-length. We prove that while only finitely many OI surfaces exist for any fixed topology, infinitely many commensurability classes arise as the topology varies. Moreover, we completely classify OI pairs of pants and OI one-holed tori, and show that their doubles are arithmetic surfaces of genus two derived from quaternion algebras over Q \mathbb {Q} .
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Mathematics and Applications
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Volume
- 379
- Issue
- 9
- Pages
- 6365–6392
- Publication date
- 8 May 2026
- Language
- EN