CONFORMALLY-DIFFERENTIAL GEOMETRY OF SUBMANIFOLDS

摘要

A conformal space C_n of dimension n is an n-dimensional Euclidean space E_n completed by a single improper point; in this space the group of point transformations transforming each hypersphere into a hypersphere is denned. This group preserves the angles between the directions and is called the conformal transformation group L of the space C_n. The generating elements of the conformal space C_n are points (hyperspheres of zero radius), hyperspheres (of real and imaginary radii), and hyperplanes of the Euclidean space E_n, which are considered as hyperspheres passing through the improper point.