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Curves with continuous Curvatures in Euclidean spaces

Published online by Cambridge University Press:  17 April 2009

Vitaly Ushakov
Vitaly Ushakov
Affiliation:
Department of MathematicsThe University of Melbourne, Parkville Vic 3052Australia, e-mail: [email protected]
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Abstract

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A class of curves of minimal smoothness for which one can build the Frenet frame, Frenet's formulae and osculating planes is described.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 393 - 401
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Hartman, Ph. and Wintner, A., ‘On the fundamental equations of differential geometry’, Amer. J. Math. 72 (1950), 757–774.Google Scholar
[2]Spivak, M., A comprehensive introduction to differential geometry II (Publish or Perish, Inc., Berkeley, 1979).Google Scholar
[3]Wintner, A., ‘On Frenet's equations’, Amer. J. Math. 78 (1956), 349–356.CrossRefGoogle Scholar