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SMYTH SURFACES AND THE DREHRISS

Published online by Cambridge University Press:  15 September 2005

John M. Burns
Affiliation:
Department of Mathematics, National University of Ireland Galway, University Road, Galway, Ireland (john.burns@nuigalway.ie)
Michael J. Clancy
Affiliation:
School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland (michael.clancy@dcu.ie)
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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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2005