Billiard in a triangle and quadratic homogeneous foliations on C2

This Note is partly an announcement. We describe the geodesic foliation of the translation surface associated to a triangular billiard in terms of real and holomorphic foliations defined by quadratic homogeneous vector fields on C-2. Our technique allows, in particular, to state the existence of real foliations by curves on C-2 arising from homogeneous quadratic vector fields and having a dense set of periodic orbits.