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

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.