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On general curves lying on a quadric

Published online by Cambridge University Press:  20 January 2009

H. F. Baker
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Introduction. The present note, though in continuation of the preceding one dealing with rational curves, is written so as to be independent of this. It is concerned to prove that if a curve of order n, and genus p, with k cusps, or stationary points, lying on a quadric, Ω, in space of any number of dimensions, is such that itself, its tangents, its osculating planes, … , and finally its osculating (h – 1)-folds, all lie on the quadric Ω, then the number of its osculating h-folds which lie on the quadric is

Two proofs of this result are given, in §§ 4 and 5.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 1 , Issue 1 , May 1927 , pp. 19 - 30
Copyright
Copyright © Edinburgh Mathematical Society 1927

References

page 19 note 1 Proc. Edin. Math. Soc, XLIV, 1926, p. 131.Google Scholar

page 25 note 1 For instance, if we can have a rational quintic curve, with its tangents, lying upon a quadric in space of four dimensions (n = 5, h = 2, r = 4), the result of the formula would otherwise be that there are two of its osculating planes upon the quadric. In the preceding paper, dealing with rational curves, we have supposed the curve of order n to lie in space of n dimensions.