Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
HELICOIDAL SURFACES WITH CONSTANT MEAN CURVATURE
MANFREDO P. DO CARMOMARCOS DAJCZER
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1982 Volume 34 Issue 3 Pages 425-435

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Abstract

We describe the space ∑\ olimits_H of all surfaces in {R^3} that have constant mean curvature H \ e 0 and are invariant by helicoidal motions, with a fixed axis, of {R^3}. Similar to the case ∑\ olimits_0 of minimal surfaces ∑\ olimits_H behaves roughly like a circular cylinder where a certain generator corresponds to the rotation surfaces and each parallel corresponds to a periodic family of isometric helicoidal surfaces.

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