Characterization of the helicoid as ruled surface with pointwise 1-type Gauss map (Q2770343)

The authors say that a ruled surface \(M\subset E^3\) has pointwise 1-type Gauss map \(G: M\to S^2\) if it satisfies \(\Delta G=fG\) with some real valued function \(f\). Here \(\Delta\) stands for the Laplace operator corresponding to the induced metric on \(M\) and \(S^2\) stands for the unit sphere in the Euclidean 3-space \(E^3\) centered at the origin. The main result is as follows: A ruled surface in \(E^3\) with pointwise 1-type Gauss map is an open portion of either a plane, or a circular cylinder, or a minimal helicoid.