Hausdorff dimension of divergent diagonal geodesics on product of finite-volume hyperbolic spaces

In this paper, we consider the product space of several non-compact finite-volume hyperbolic spaces, V₁,V₂,… ,Vₖ of dimension n . Let T¹(Vᵢ) denote the unit tangent bundle of Vᵢ and gₜ denote the geodesic flow on T¹(Vᵢ) for each i=1,… ,k . We define $${eqnarray}{D}ₖ:=\{(v₁,… ,vₖ)\,∈ \,T¹(V₁)× ⋯ × T¹(Vₖ)\,:\,(gₜ(v₁),… ,gₜ(vₖ)) diverges as t→ ∞ \}.{eqnarray}$$ We will prove that the Hausdorff dimension of ${D}ₖ$ is equal to $k(2n-1)-((n-1)/2)$ . This extends a result of Cheung.