THE SPACE OF SUPER LIGHT RAYS FOR COMPLEX CONFORMAL SPACETIMES

After defining a superconformal structure on a 4\4N supermanifold, its space of super light rays is constructed and shown to have a natural supercontact structure. We next construct, for a 5\2N dimensional supe rcontact manifold, its space of normal quadrics. This is shown to be a 4\4N superconformal manifold. Every four dimensional conformal manifo ld is then proved to have an extension to a superconformal manifold of dimension 4\4N for N less-than-or-equal-to 4. After the equivalence o f the N = 3 Supersymmetric Yang-Mills equations and integrability alon g super light rays is shown, a one to one correspondence between solut ions to the N = 3 Supersymmetric Yang-Mills equations and certain vect or bundles over the N = 3 space of super light rays is established.