On Fenchel's problem
The author considers the problem to find a criterion for the closedness of a curve of length \(\omega\) on a unit sphere in \(E^3\) by its geodesic curvature \(k(t)\) as a function of the natural parameter \(t\). This problem is related to Fenchel's problem of constructing criteria for the closedness of a space curve by given curvature and torsion as functions of the natural parameter. In this context the author proves two theorems and confirms the opinion that it is impossible to solve Fenchel's problem effectively.
scientific article; zbMATH DE number 830755