Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-06T11:40:52.280Z Has data issue: false hasContentIssue false

Osculating Spaces

Published online by Cambridge University Press:  20 November 2018

Peter Scherk*
Affiliation:
University of Toronto and The Summer Research Institute of the Canadian Mathematical Congress
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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, 296302.Google Scholar