Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 459, Issue 2038, Pages 2449-2462Publisher
ROYAL SOC
DOI: 10.1098/rspa.2003.1135
Keywords
shell membrane; integrability; Dupin cyclides; Backlund transformation; O surfaces
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It is established that a well-known system of classical shell theory descriptive of membranes in equilibrium is, in fact, integrable. The membranes are shown to have geometries within the integrable class of so-called O surfaces. The membrane O surfaces include inter alia minimal, constant mean curvature, constant Gaussian curvature and, more generally, linear Weingarten surfaces, as well as canal surfaces and Dupin cyclides.
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