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Zur Möbiusgeometrie der Kurventheorie

On the conformal geometry of spacecurves

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Abstract

Using the derivational formulas for stripes we derive in section 1 the derivational formulas for spacecurves in three-dimensional conformal spaceM 3. With a curve we associate locally a one-parameter family of so calledQ 4-surfaces having contact of order 5. AQ 4-surface is generated by two special parabolic pencils of spheres. We investigate alsoQ 4-surfaces having contact of orderk(k=7,8). Section 2 deals with isogonal-trajectories on the surface of the principal circles of the given spacecurve. We avoid invariant parameters as used in projective geometry for getting results of conformal geometry.

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Literatur

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

    A. Pendl

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  1. A. Pendl
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Pendl, A. Zur Möbiusgeometrie der Kurventheorie. Monatshefte für Mathematik 81, 141–148 (1976). https://doi.org/10.1007/BF01301238

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  • DOI: https://doi.org/10.1007/BF01301238

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