Remark on isotropic four dimensional conformal structures

In the present paper we explain different types of four dimensional structures, Hodge operator and their generalizations. Completely isotropic four dimensional (4D) conformal structures and conformal structure in a 4D-hypersursurface are investigated. We establish the self dual, anti-self-dual and conformally flat properties of four dimensional conformal structures in its principal planes. We prove that if four dimensional hypersurface caries two fundamental completely isotropic submanifolds then it is a two dimensional-plane, two dimensionaldevelopable surface and tangentially nondegenerate submanifold having four dimensional-osculating subspace carrying a conjugate net. Here it is investigated that the integral curves of each of four families of real principal directions on a manifold M endowed with four dimensional pseudoconformal structure i.e. CO(1, 3)-structure are isotropic geodesics of the manifold M