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Osculating Spaces

Published online by Cambridge University Press:  20 November 2018

Peter Scherk
Peter Scherk*
Affiliation:
University of Toronto and The Summer Research Institute of the Canadian Mathematical Congress
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In this paper an attempt is made to prove some of the basic theorems on the osculating spaces of a curve under minimum assumptions. The natural approach seems to be the projective one. A duality yields the corresponding results for the characteristic spaces of a family of hyperplanes. A duality theorem for such a family and its characteristic curve also is proved. Finally the results are applied to osculating hyperspheres of curves in a conformai space.

The analytical tools are collected in the first three sections. Some of them may be of independent interest.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 669 - 684
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Milne-Thomson, L. M., The calculus of finite differences, London (1933).Google Scholar
2. Schwarz, H. A., Verallgemeinerung eines analytischen Fundamentalsatzes, Mathematische Abhandlungen, Berlin (1890), II, 296–302.Google Scholar