In Y = SO_3(R) SL_3(R)/Γ with Γ torsion-free and commensurable with SL_3(Z), the set of directions yielding bounded geodesics from any y is hyperplane absolute winning.
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Bounded Geodesics on Locally Symmetric Spaces
In Y = SO_3(R) SL_3(R)/Γ with Γ torsion-free and commensurable with SL_3(Z), the set of directions yielding bounded geodesics from any y is hyperplane absolute winning.