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Zur Möbiusgeometrie der Berührkreisscharen

On the conformal geometry of one-parameter families of tangent circles

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Abstract

Making use of an earlier result of the theory of stripes in three-dimensional conformal spaceM 3 we obtain a moving frame and derivational formulas for one-parameter families of tangent circles inM 3. Avoiding invariant parameters we can set up a bijection of the tangent circles into the osculating circles that preserves the duple ratio. The following section deals with loxodromes on Dupin cyclides. Finally with the aid of a modified stereographic projection we show how to get the Frenet formulas of the euclidian theory of spacecurves from the derivational formulas for tangent circles inM 3.

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  1. Fakultät für Mathematik, Kaiserstraße 12, D-7500, Karlsruhe, Bundesrepublik Deutschland

    A. Pendl

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  1. A. Pendl
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Pendl, A. Zur Möbiusgeometrie der Berührkreisscharen. Monatshefte für Mathematik 80, 307–318 (1975). https://doi.org/10.1007/BF01472578

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  • DOI: https://doi.org/10.1007/BF01472578

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