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arXiv · 2503.14007

Bounded Geodesics on Locally Symmetric Spaces

Lifan Guan·Chengyang Wu
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Abstract

Let $\Gamma$ be a torsion-free subgroup of $SL_3(R)$ commensurable with $SL_3(Z)$, and $Y=SO_3(R)\backslash SL_3(R)/\Gamma$ be endowed with the natural locally symmetric space structure. We prove that for any point y in 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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Lifan Guan, Chengyang Wu. 2025-03-18. Bounded Geodesics on Locally Symmetric Spaces. https://doi.org/10.1017/etds.2026.10298

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