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A short proof of the generalized Bonnet theorem
Author(s) -
Kanbay Filiz
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2909
Subject(s) - mathematics , euclidean geometry , euclidean space , geodesic , space (punctuation) , constant (computer programming) , surface (topology) , pure mathematics , mathematical analysis , geometry , linguistics , philosophy , computer science , programming language
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 [4][Hagen H, 1983] is given. Copyright © 2013 John Wiley & Sons, Ltd.