Helicoids of constant mean curvature and their Gauss maps (Q796129)

The author gives a description, via the theory of harmonic maps, of Gauss maps of all complete helicoidal surfaces with constant mean curvature in \(R^ 3\); the latter surfaces were described by the reviewer and \textit{M. Dajczer} [Tohôku Math. J., II. Ser. 34, 425-435 (1982; Zbl 0501.53003)]. As a consequene of the above, the author shows that the spherical image of a complete helicoidal surface with constant mean curvature in \(R^ 3\) contains an equator.