Vol. 40, No. 2, 1972

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Approximation of curves

Heinrich W. Guggenheimer

Vol. 40 (1972), No. 2, 301–303
Abstract

Generalizing recent results of J. M. Sloss we show: A curve in n-space that admits a continuously differentiable first order frame can be C1 approximated to any desired accuracy by a continuous, piecewise Cr+2 curve for which the curvature functions are prescribed Cr(r = 0,1,,) functions of the arc length. The result can be extended to riemannian geometry.

Mathematical Subject Classification 2000
Primary: 53A05
Milestones
Received: 23 October 1970
Published: 1 February 1972
Authors
Heinrich W. Guggenheimer