A short proof of the generalized Bonnet theorem


Kanbay F.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.37, no.10, pp.1488-1490, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 10
  • Publication Date: 2014
  • Doi Number: 10.1002/mma.2909
  • Title of Journal : MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Page Numbers: pp.1488-1490

Abstract

In three-dimensional Euclidean space E3, the Bonnet theorem says that a curve on a ruled surface in three-dimensional Euclidean space, having two of the following properties, has also a third one, namely, it can be a geodesic, that it can be the striction line, and that it cuts the generators under constant angle. In this work, in n dimensional Euclidean space En, a short proof of the theorem generalized for (k+1) dimensional ruled surfaces by Hagen in is given. Copyright (c) 2013 John Wiley & Sons, Ltd.