Approximation of curves

Heinrich W. Guggenheimer

Vol. 40 (1972), No. 2, 301–303

DOI: 10.2140/pjm.1972.40.301

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 C^r+2 curve for which the curvature functions are prescribed C^r(r = 0,1,⋯,∞,ω) 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