A characterization of conformal mappings in \(\mathbb{R}^4\) by a formal differentiability condition (Q2730920)
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scientific article; zbMATH DE number 1625244
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of conformal mappings in \(\mathbb{R}^4\) by a formal differentiability condition |
scientific article; zbMATH DE number 1625244 |
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3 February 2003
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conformal mappings
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Möbius transformations
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quaternionic analysis
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differentiability
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0.8656404
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0.8618471
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0.86102194
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0.8602412
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0.85826254
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0.8579463
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A characterization of conformal mappings in \(\mathbb{R}^4\) by a formal differentiability condition (English)
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After giving a short review on quaternionic differentiability, in particular, the description via quaternionic differential forms, the authors proceed to conformal mappings in \({\mathbb R}^4.\) In contrast to the two-dimensional case, every conformal mapping is a Möbius transformation and thus can be represented as composition of simple geometric mappings. As Gauss' definition of conformal mappings is based on differentials, the authors succeed in proving a local characterization of quaternionic conformal mappings by a system of partial differential equations, making use of orthonormal moving frames. Then the frame functions are connected to the quaternionic parameters describing the corresponding Möbius transformation.
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