  Let H be the hyperbolic space of dimension n+1. A geodesic foliation of H is
given by a smooth unit vector field on H all of whose integral curves are
geodesics. Each geodesic foliation of H determines an n-dimensional submanifold
M of the 2n-dimensional manifold L of all the oriented geodesics of H (up to
orientation preserving reparametrizations). The space L has a canonical split
semi-Riemannian metric induced by the Killing form of the isometry group of H.
Using a split special Lagrangian calibration, we study the volume maximization
problem for a certain class of geometrically distinguished geodesic foliations,
whose corresponding submanifolds of L are space-like.
