Vol. 110, No. 2, 1984

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Helicoids of constant mean curvature and their Gauss maps

Walter Iaan Seaman

Vol. 110 (1984), No. 2, 387–396

A helicoidal surface in R3 is a natural generalization of a surface of revolution. We give a simple description via the theory of harmonic maps of the Gauss maps and Gaussian images of complete helicoidal surfaces of constant mean curvature in R3. Do Carmo had conjectured that the Gaussian image of such a surface contained an equator. This is true for the complete surfaces of revolution of constant mean curvatures in R3 and we affirm this for helicoids of constant mean curvature.

Mathematical Subject Classification 2000
Primary: 53A10
Received: 11 November 1982
Published: 1 February 1984
Walter Iaan Seaman