Abstract
Abstract In three‐dimensional Euclidean space E 3 , 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 E n , a short proof of the theorem generalized for ( k + 1) dimensional ruled surfaces by Hagen in is given. Copyright © 2013 John Wiley & Sons, Ltd.
Keywords
Mathematics
Euclidean geometry
Euclidean space
Geodesic
Space (punctuation)
Constant (computer programming)
Surface (topology)
Pure mathematics
Mathematical analysis
Geometry
Subject Areas
Geometric Analysis and Curvature Flows
·Applied Mathematics ·Physical Sciences
Advanced Differential Geometry Research
·Astronomy and Astrophysics ·Physical Sciences
Geometry and complex manifolds
·Geometry and Topology ·Physical Sciences
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