Bulletin de la Société Royale des Sciences de Liège vol:70 issue:1 pages:35-49
We show that conformal mappings in $R^4$ can be characterized by a formal differentiability condition. The notion of differentiability described in this paper generalizes the classical concept of differentiability in the sense of putting the differential of a function into relation with variable differential forms of first order.
This approach provides further an application of the use of those arbitrary orthonormal sets which are used in works of V. Kravchenko, M. Shapiro and N. Vasilevski on quaternionic analysis. However, it is crucial to consider variable orthonormal sets, so-called moving frames.