Osaka Journal of Mathematics

Singularities of the asymptotic completion of developable Möbius strips

Kosuke Naokawa

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Abstract

We prove that the asymptotic completion of a developable Möbius strip in Euclidean three-space must have at least one singular point other than cuspidal edge singularities. Moreover, if the strip is generated by a closed geodesic, then the number of such singular points is at least three. These lower bounds are both sharp.

Article information

Source
Osaka J. Math., Volume 50, Number 2 (2013), 425-437.

Dates
First available in Project Euclid: 21 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1371833493

Mathematical Reviews number (MathSciNet)
MR3080808

Zentralblatt MATH identifier
1275.53009

Subjects
Primary: 53A05: Surfaces in Euclidean space 57R45: Singularities of differentiable mappings

Citation

Naokawa, Kosuke. Singularities of the asymptotic completion of developable Möbius strips. Osaka J. Math. 50 (2013), no. 2, 425--437. https://projecteuclid.org/euclid.ojm/1371833493


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