Multiple intersections on negatively curved surfaces (Q756164)

Let X be a compact surface with a Riemannian metric of negative curvature. An n-cross on X consists of n unit tangent vectors of X with the same foot point. An n-tuple point of X consists of a point on X together with n unit vectors at that point which are tangent vectors to the same unit speed geodesic (not necessarily closed). The authors show that the quadruple points on X are dense in the space of 4-crosses.