Geodesic
On Differentiable Arcs and Curves, VI: Singular Osculating Spaces of Curves of Order n + 1 in Projective n-Space
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 1042-1061

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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. 
Scherk, Peter. On Differentiable Arcs and Curves, VI: Singular Osculating Spaces of Curves of Order n + 1 in Projective n-Space. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 1042-1061. doi: 10.4153/CJM-1967-095-7
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