A characterization of conformal mappings in by R4 formal differentiability condition
Vakgroep Wiskundige Analyse, Universiteit Gent, Galglaan 2, B-9000 Gent, Belgium, krauss@cage.rug.ac.be
Departemento de Matemática, Universidade de Aveiro, Campus Universitário Santiago, P-3810-193 Aveiro, Portugal, hrmalon@mat.ua.pt
Abstract
We show that conformal mappings in R4 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.