Osaka Journal of Mathematics

Singularities of the asymptotic completion of developable Möbius strips

Kosuke Naokawa

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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

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

First available in Project Euclid: 21 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Naokawa, Kosuke. Singularities of the asymptotic completion of developable Möbius strips. Osaka J. Math. 50 (2013), no. 2, 425--437.

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