On Differentiable Arcs and Curves, VI: Singular Osculating Spaces of Curves of Order n + 1 in Projective n-Space

Abstract

A closed curve Kn+1 of order n + 1 in real projective n-space Rn has a maximum number of n + 1 points in common with any (n — 1)-space. These curves are subjected to certain differentiability assumptions which make it possible to describe their singular points and to provide them with multiplicities in analogy with algebraic geometry.