Bulletin de la Société Royale des Sciences de Liège

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Rolf Sören KRAUSSHAR & Helmuth Robert MALONEK

A characterization of conformal mappings in by R4 formal differentiability condition

(Volume 70 - Année 2001 — Numéro 1)
Article
Open Access
Mots-clés : conformal mappings, Möbius transformations, quaterionic analysis, differentiability

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.

To cite this article

Rolf Sören KRAUSSHAR & Helmuth Robert MALONEK, «A characterization of conformal mappings in by R4 formal differentiability condition», Bulletin de la Société Royale des Sciences de Liège [En ligne], Volume 70 - Année 2001, Numéro 1, 35 - 49 URL : http://popups.ulg.be/0037-9565/index.php?id=1398.

About: Rolf Sören KRAUSSHAR

Vakgroep Wiskundige Analyse, Universiteit Gent, Galglaan 2, B-9000 Gent, Belgium, krauss@cage.rug.ac.be

About: Helmuth Robert MALONEK

Departemento de Matemática, Universidade de Aveiro, Campus Universitário Santiago, P-3810-193 Aveiro, Portugal, hrmalon@mat.ua.pt