Decomposition of the Darboux rotation into two plane rotations
type: Item
instance of: scholarly article
title: Decomposition of the Darboux rotation into two plane rotations
zbMATH Open document ID: 0782.53002
DOI: 10.1007/BF01223802
author: Johann Hartl
published in: Journal of Geometry
publication date: 1993-10-13T00:00:00Z
review text: The Darboux rotation of the Frenet frame of a Frenet curve in 3-space is decomposed into two simultaneous rotations which can be coupled by a simple mechanism. From this point of view solutions of the Frenet equations are discussed. In particular, a necessary condition is obtained for a space curve in terms of its invariants in order to be closed.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53A17
zbMATH DE Number: 428593
zbMATH Keywords: Darboux rotation
zbMATH Keywords: Frenet frame
zbMATH Keywords: Frenet curve
reviewed by: Bernd Wegner
MaRDI profile type: Publication
cites work: Conditions for polygonal lines and polyhedra in \(E^ 3\) to be closed
cites work: On the differential geometry of closed space curves
cites work: Über direkt integrierbare Kurven und strenge Böschungskurven im \(R^ n \)sowie geschlossene verallgemeinerte Hyperkreise
cites work: A Differential-Geometric Criterion for a Space Curve to be Closed
cites work: Notwendige und hinreichende Bedingungen dafür, daß eine Raumkurve geschlossen ist
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description: scientific article; zbMATH DE number 428593