Sides of the Möbius strip
type: Item
instance of: scholarly article
title: Sides of the Möbius strip
zbMATH Open document ID: 0864.53002
DOI: 10.1007/BF01268871
author: Peter Røgen
author: Thomas Randrup
published in: Archiv der Mathematik
publication date: 1997-06-17T00:00:00Z
review text: The paper presents necessary and sufficient conditions for a curve to be the unique center curve of an analytic and flat embedding of the Möbius strip (or the orientable cylinder) into Euclidean 3-space. Using these conditions, we extend an example of G. Schwarz into a continuous family of analytic and flat Möbius strips. This family is split into two connected components. We give a topological argument that explains this behaviour. Finally, we draw the connection to the work of C. Chicone and N. J. Kalton on flat and analytic Möbius strips. This points towards a connection between a linking number and the total torsion of the orthogonal axis of a Möbius strip.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 58D10
zbMATH DE Number: 938566
zbMATH Keywords: center curves of Möbius strips
zbMATH Keywords: flat and analytic embeddings of Möbius strips
zbMATH Keywords: linking number
zbMATH Keywords: total torsion
MaRDI profile type: Publication
cites work: Q4779598
cites work: Differential forms. With applications to the physical sciences
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cites work: A pretender to the title ``canonical Möbius strip''
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description: scientific article; zbMATH DE number 938566