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SMYTH SURFACES AND THE DREHRISS

Published online by Cambridge University Press:  15 September 2005

John M. Burns  and
Michael J. Clancy
John M. Burns
Affiliation:
Department of Mathematics, National University of Ireland Galway, University Road, Galway, Ireland ([email protected])
Michael J. Clancy
Affiliation:
School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland ([email protected])
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Abstract

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Isometric deformations of immersed surfaces in Euclidean 3-space are studied by means of the drehriss. When the immersion is of constant mean curvature and the deformation preserves the mean curvature, we determine the drehriss explicitly in terms of the immersion and its Gauss map. These methods are applied to obtain an alternative classification of the Smyth surfaces, i.e. constant mean curvature immersions of the plane into Euclidean 3-space which admit the action of $S^1$ as a non-trivial group of internal isometries.

Keywords

Primary 3A10surfacesconstant mean curvatureisometric deformationsDelaunay
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 3 , October 2005 , pp. 549 - 555
Copyright
Copyright © Edinburgh Mathematical Society 2005