A Property of the Curvature and Torsion of a Regular Family of Curves in $E^n$

M. G. Szajewska

Institute of Mathematics, University of Bialystok

Abstract: In is proved that, for a regular family of algebraic curves in $E^n$, there exists a sequence of points at which all but the last curvature of the curves simultaneously tend to zero.

Keywords: regular family of algebraic curves, mean curvature, Gaussian curvature, curvature and torsion of an algebraic curve, Bianchi coordinate system.

UDC: 514

Received: 31.10.2006
Revised: 01.10.2007

DOI: 10.4213/mzm4718

 English version: Mathematical Notes, 2008, 83:5, 688–692

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