A short proof of the generalized Bonnet theorem

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.