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Parameterisation of developable surfaces by asymptotic lines

Published online by Cambridge University Press:  17 April 2009

Vitaly Ushakov
Vitaly Ushakov
Affiliation:
Department of Mathematics, The University of Melbourne, Parkville, Vic 3052, Australia, e-mail: [email protected]
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Abstract

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An example of a “non-developable” surface of vanishing Gaussian curvature from W. Klingenberg's textbook is considered and its place in the theory of 2-dimensional developable surfaces is pointed out. The surface is found in explicit form. Other examples of smooth developable surfaces not allowing smooth asymptotic parametrisation are analysed. In particular, Hartman and Nirenberg's example (1959) is incorrect.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 411 - 421
Copyright
Copyright © Australian Mathematical Society 1996

References

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