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Über direkt integrierbare Kurven und strenge Böschungskurven im ℝn sowie geschlossene verallgemeinerte Hyperkreise

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Abstract

A curve in Euclidean space ℝn is called “directly integrable”, if it can be explicitly calculated from the curvatures in a specified way. A necessary and sufficient condition for a curve to be directly integrable is that all its curvatures are real multiples of a single real function. Directly integrable curves in an odd-dimensional space ℝn (n=2q+1) can be interpreted as generalized helices. In the case of even-dimensional space ℝn (n=2p), we give a simple necessary and sufficient condition for a directly integrable curve to be closed.

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  1. Mathematisches Institut der Technischen Universität, Postfach 20 24 20, D-8000, München 2

    Johann Hartl

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  1. Johann Hartl
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Hartl, J. Über direkt integrierbare Kurven und strenge Böschungskurven im ℝn sowie geschlossene verallgemeinerte Hyperkreise. Manuscripta Math 42, 273–284 (1983). https://doi.org/10.1007/BF01169589

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