Invariante Konstruktion der Geometrie einer Hyperfläche in einem konformen Raum

Abstract

A partly expository paper on conformal differential geometry of a hypersurface. The first three sections are introductory and are devoted to multispherical coordinate representation and the study of the subgroups of the conformal group leaving the surface element invariant. In the next four sections is given an invariant construction of the theory by means of the stationary subgroups associated with the hypersurface. By this means it is possible to introduce conformal tensors gij, aij, cij and Bk = bijkaij which determine the hypersurface within a conformal mapping. The remainder of the paper is devoted to some special problems dealing with the order of contact of certain cyclides with the hypersurface, particularly for the critical cases of the envelopping space being of 3 and 4 dimensions.