Bounded Geodesics on Locally Symmetric Spaces

Let $\mathrm{\Gamma }$ be a torsion-free subgroup of $S{L}_3(R)$ commensurable with $S{L}_3(Z)$, and $Y=S{O}_3(R)\mathrm{\backslash }S{L}_3(R)\mathrm{/}\mathrm{\Gamma }$ 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.