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A Remarkable Class of Mannheim-Curves

Published online by Cambridge University Press:  20 November 2018

Richard Blum
Richard Blum*
Affiliation:
University of Saskatchewan and Summer Research Institute of the Canadian Mathematical Congress
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It is well known that the determination of a (non-isotropic) curve in the euclidean 3-space with given curvature κ(S) and torsion τ(s), where s represents the arc-length, depends upon the integration of a Riccati equation; and that this can be performed only if a particular integral of the equation is known.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 2 , June 1966 , pp. 223 - 228
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Struik, D.J., Differential Geometry. Cambridge, Mass. (1950).Google Scholar
2. Mannheim, A., Paris C. R. 86 (1878), p. 1254-1256.Google Scholar
3. Scheffers, G., Theorie der Kurven, Leipzig (1901), p. 252-253.Google Scholar
4.Encyklopädie der Mathematischen Wissenschaften III/3, p. 246.Google Scholar