This talk is the second part of a report on joint work with Wojciech Kryński, following a talk given on April 15.

Cone structures on differentiable manifolds are defined as fields of cones in the tangent bundle. A cone structure is isotrivial, modeled on a given projective variety, if the cones at each point of the manifold are projectively equivalent to that variety. We study integrable cone structures, which arise naturally from ordinary differential equations via a canonical construction. We prove that isotrivial, integrable cone structures modeled on generic curves in n-dimensional projective space or on ruled surfaces in three-dimensional projective space are necessarily flat. We provide applications of the results to integrable systems and causal geometry.