ABSTRACT
In the previous chapter we proved that any great circle of the unit sphere meets the spherical indicatrix of a closed space curve l?, it means that the spherical indicatrix does not belong to any hemisphere. This necessary condition was first discovered by E. Poznjak when he was a post-graduate student of Vygodsky. We will discuss the following problem: Let y he u closed curve on the unit sphere. Does there exist a closed curve l? such that y is the spherical indicatrix of r? It was observed that the mentioned necessary condition is sufficient.
