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Connexions and Prolongations

Published online by Cambridge University Press:  20 November 2018

Leif-Norman Patterson
Leif-Norman Patterson*
Affiliation:
University of Tromsø, Tromsø Norway
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Computation of the velocity of a given motion depends on measurement of nearby position changes only. Computation of acceleration, on the other hand, depends on measurement of nearby changes in velocity. But since velocity vectors are attached to positions so that even nearby ones are not a priori comparable, acceleration is not computable until a rule for comparison of vectors along a curve is given. Such a rule-parallel translation or linear connexion - exists automatically in Euclidean spaces. For motions in more general manifolds, for example (semi-) Riemannian ones, parallel translation is a less obvious consequence of the metric properties.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 766 - 791
Copyright
Copyright © Canadian Mathematical Society 1975

References

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