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Conical Differentiation

Published online by Cambridge University Press:  20 November 2018

N. D. Lane  and
K. D. Singh
N. D. Lane
Affiliation:
McMaster University, and University of Toronto
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This paper follows naturally a note on parabolic differentiation (2) in which the parabolically differentiable points in the real affine plane were discussed. In the parabolic case, the four-parameter family of parabolas in the affine plane led to three differentiability conditions. In the present paper, the five-parameter family of conies in the real projective plane gives rise to four differentiability conditions and a point of an arc in the projective plane is called conically differentiable if these four conditions are satisfied. The differentiable points are classified by the nature of their families of osculating conies, superosculating conies, and their ultraosculating conies.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 169 - 190
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Bol, G., Projektive Differentialgeometrie (Göttingen, 1954).Google Scholar
2. Lane, N. I., Parabolic differentiation, Can. J. Math., 15 (1963), 546–562.Google Scholar