EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 43(57), pp. 137--142 (1988)

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A geometric characterization of helicodial surfaces of constant mean curvature

Ioannis M. Roussos

Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688, USA

Abstract: We prove that a helicodial surface has constant mean curvature if and only if its principal axes make an angle constant with the orbits. Moreover, the arguments used lead to a simple proof of the fact that all helicodial surfaces with constant mean curvature $H$ can be isometrically deformed, trough helicodial surfaces of the same $H$, into surfaces of revolution of the same $H$ (Delaunay surfaces).

Classification (MSC2000): 53A05

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