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On Differentiable Arcs and Curves, VI: Singular Osculating Spaces of Curves of Order n + 1 in Projective n-Space
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1967
References
1.
Haupt, O., Ein Satz ilber die reellen Raumkurven vierter Ordnung und seine Verallgemeinerung, Math. Ann.,
108 (1933), 126–142.Google Scholar
2.
Pohl, Wm. F., On a theorem related to the four-vertex theorem, Ann. of Math.,
84 (1966), 356–367.Google Scholar
3.
Scherk, P., Ueber differenzierbare Kurven und Bögen III. Ueber Punkte (n + 1)-ter Ordnung auf Bögen im Rn
, Annali di Mat. (4),
17 (1938), 291–305.Google Scholar
4.
Scherk, P., On differentiable arcs and curves IV. On the singular points of curves of order n + 1 in projective n-space, Ann. of Math.,
46 (1945), 68–82.Google Scholar
5.
Scherk, P., same title IVa. On certain singularities of curves of order n + 1 in projective n-space, Ann. of Math.,
46 (1945), 175–181.Google Scholar
6.
Scherk, P., same title V. On a class of mappings of the curves of order n + 1 in projective n-space into themselves, Ann. of Math.,
47 (1946), 786–805.Google Scholar
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