PreprintCC BY 4.0arXiv
Complex hyperbolic surfaces whose closed geodesics are all simple
Abstract
We show that all closed geodesics in any arithmetic complex hyperbolic surface of second type are simple. These include the fake projective planes studied by Mumford, Klingler, Prasad-Yeung, and Cartwright-Steger.
Related
- Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds
- Simple geodesics in closed hyperbolic manifolds
- Sharp effective equidistribution of closed geodesics in compact hyperbolic surfaces
- Lengths of closed geodesics on random non-compact hyperbolic surfaces
- The Non-Abelian X-Ray Transform on Simple Asymptotically Hyperbolic Surfaces
BibTeX
@misc{douba2026complex,
title = {{Complex hyperbolic surfaces whose closed geodesics are all simple}},
author = {Sami Douba and D. B. McReynolds and Julien Paupert and Jonathan Vittore},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01806},
eprint = {2610.01806},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01806},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Complex hyperbolic surfaces whose closed geodesics are all simple
AU - Sami Douba
AU - D. B. McReynolds
AU - Julien Paupert
AU - Jonathan Vittore
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01806
UR - https://arxiv.org/abs/2610.01806
AB - We show that all closed geodesics in any arithmetic complex hyperbolic surface of second type are simple. These include the fake projective planes studied by Mumford, Klingler, Prasad-Yeung, and Cartwright-Steger.
ER -