ABSTRACT
Efimov, Fenchel and other geometers independently studied the following problem: what are the necessary and sufficient conditions on the curvature and torsion o f a space curve in order for the curve to be closed? It is assumed that the curvature k(s) and torsion IF.(S) are functions of the arc length S. Fenchel thought that this question is the most important one in the theory of closed curves.
