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Developable surfaces in Euclidean space

Part of: Classical differential geometry

Published online by Cambridge University Press:  09 April 2009

Vitaly Ushakov
Vitaly Ushakov
Affiliation:
Department of Mathematics, The University of Melbourne, Parkville VIC 3052, Australia e-mail: v.ushakov@ms.unimelb.edu.au
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Abstract

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The classical notion of a two-dimensional develpable surface in Euclidean three-space is extended to the case of arbitrary dimension and codimension. A collection of characteristic properties is presented. The theorems are stated with the minimal possible integer smoothness. The main tool of the investigation is Cartan's moving frame method.

Keywords

Developable surfaceplanar pointruled surfaceflat metricpoint codimension of a surfacelocal codimension of a surfaceaffinely stable immersion

MSC classification

Secondary: 53A07: Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 3 , June 1999 , pp. 388 - 402
Copyright
Copyright © Australian Mathematical Society 1999

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