Conformal and projective geometries revisited

The local study of conformal and projective structures on a manifold, initiated by H. Weyl in 1918, are revisited in the light of the modern formal theory of systems of partial differential equations and Lie pseudo groups, initiated by D.C. Spencer in 1970 and largely superseding the classical approaches of E. Cartan and M. Janet. Application is done to the computation of the number of components of useful tensors and to various inverse problems in differential geometry. (Author) 12 refs