AN ANALYSIS OF CURVES OF MINIMAL ORDER, AS REGARDS THE TYPE AND NUMBER OF SINGULAR POINTS

Abstract

The object of this dissertation is to give a classification of curves of minimal order in the real conformal and projective planes with respect to the type and number of singular points. While strongly differentiable curves of minimal order have been studied in detail, little or no research has been done on general differentiable curves of minimal order. The major emphasis lies in the analysis of these curves and the general attack utilizes the notion of the characteristic of a differentiable point. Thus in both the conformal and conical cases, the author obtains valuable information as to the structure of differentiable curves of minimal order in both the conformal and projective planes. It is only left to inquire as to the structure of such curves, if all differentiability restrictions are dropped.