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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Inverting a cylinder through isometric immersions and isometric embeddings


Authors: B. Halpern and C. Weaver
Journal: Trans. Amer. Math. Soc. 230 (1977), 41-70
MSC: Primary 58D10; Secondary 57D40
DOI: https://doi.org/10.1090/S0002-9947-1977-0474388-1
MathSciNet review: 0474388
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Abstract: It is shown that a right circular cylinder can be turned inside out through immersions which preserve its flat Riemannian metric if and only if its diameter is greater than its height. Such a cylinder can be turned inside out through embeddings which preserve its flat Riemannian metric provided its diameter is greater than $ (\pi + 2)/\pi $ times its height. A flat Möbius strip has an immersion into Euclidean three dimensional space which preserves its Riemannian metric if and only if its length is greater than $ \pi /2$ times its height.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0474388-1
Keywords: Isometric immersion, isometric embedding, homotopy, isotopy, Möbius band, flat cylinder
Article copyright: © Copyright 1977 American Mathematical Society