Using Cartan's equivalence method for point transformations we obtain from first principles the conformal geometry associated with third order ODEs and a special class of PDEs in two dimensions. We explicitly construct the null tetrads of a family of Lorentzian metrics, the conformal group in three and four dimensions and the so called normal metric connection. A special feature of this connection is that the non vanishing components of its torsion depend on one relative invariant, the (generalized) W��nschmann Invariant. We show that the above mentioned construction naturally contains the Null Surface Formulation of General Relativity.

33 pages. To be published in Class. Quantum Grav