The theory of curves in differential geometry from the viewpoint of the theory of functions of a real variable

摘要

This paper contains a brief survey of the theory of curves constructed by A. D. Aleksandrov and the author. The basic notions of the theory are defined. the statements of some of its most important results are given, and the methods of study applied in this theory are described. The principal methods are: the method based on using the notions of the tangent indicatrix of a curve in R-n and the development of a spherical curve, and the method based on integral-geometric relations of the type found by Fary and Milnor. The integral-geometric method for solving problems in the theory of curves was proposed and realized by the author.