Null Surfaces and Legendre Submanifolds
  It is shown that the main variable Z of the Null Surface Formulation of GR is the generating function of a constrained Lagrange submanifold that lives on the energy surface H=0 and that its level surfaces Z=const. are Legendre submanifolds on that energy surface.   The behaviour of the variable Z at the caustic points is analysed and a genralization of this variable is discussed. 
Mirta Iriondo, Carlos Kozameh, and Alejandra Rojas