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The parallel rank of a submanifold of Euclidean space

Published online by Cambridge University Press:  24 October 2008

A. M. Flegmann
A. M. Flegmann
Affiliation:
SD-Scicon plc, 49 Berners Street, London W1P 4AQ
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Extract

The aim of this paper is to make some remarks about the theory of parallel immersions in ℝn. We show that the existence of parallels to a curve in ℝn depends on the values of the integrals of the n − 1 curvature functions along the curve. We then give examples of immersions of S1 in ℝ3 and of immersions of codimension 2 with local parallel rank zero, thereby answering certain questions in [1].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 1 , July 1989 , pp. 89 - 93
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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