We first describe the numerical invariants attached to the second fundamental
form of a spacelike surface in four-dimensional Minkowski space. We then study
the configuration of the nu-principal curvature lines on a spacelike surface,
when the normal field nu is lightlike (the lightcone configuration). Some
observations on the mean directionally curved lines and on the asymptotic lines
on spacelike surfaces end the paper.Comment: 27 page