On area stationary surfaces in the space of oriented geodesics of hyperbolic 3-space - Georgiou, Nikos (MATHEMATICA SCANDINAVICA, 2012)
We study area-stationary surfaces in the space L(H^3) of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. We prove that every holomorphic curve in L(H^3) is an area-stationary surface. We then classify Lagrangian area-stationary surfaces Σ in L(H^3) and prove that the family of parallel surfaces in H^3 orthogonal to the geodesics γΣ form a family of equidistant tubes around a geodesic. Finally we find an example of a two parameter family of rotationally symmetric area-stationary surfaces that are neither Lagrangian nor holomorphic.