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Bounded geodesics on locally symmetric spaces | Synapse

April 10, 2026

Bounded geodesics on locally symmetric spaces

Key Points

The aim is to study the bounded geodesics from a specific point in a locally symmetric space derived from SL3.
Defined the locally symmetric space structure on Y using SL3 and SO3.
Analyzed the directions of geodesic rays from points in Y.
Established the hyperplane absolute winning property for bounded directions.
Showed that the set of directions for bounded geodesic rays is a hyperplane.
Demonstrated this property holds for any point y in the defined space Y.

Abstract

Abstract Let be a torsion-free subgroup of SL₃ (R) commensurable with SL₃ (Z), and Y= SO₃ (R) SL₃ (R) / be endowed with the natural locally symmetric space structure. We prove that for any point y Y, the set of directions in which the geodesic ray starting from y is bounded in Y, is hyperplane absolute winning.

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Authors

L

Lifan Guan

C

C.-Y. Wu

Journals

Ergodic Theory and Dynamical Systems

Actions

Institutions

Peking University

Westlake University

References and Citations

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Cite this study

Guan et al. (Tue,) studied this question.

www.synapsesocial.com/papers/69d895046c1944d70ce05ec8 — DOI: https://doi.org/10.1017/etds.2026.10298