Surfaces with 1-type Gauss map (Q2365355)

The author proves the following theorem. Let \(M\) be an orientable connected surface of Euclidean 3-space \(E^3\). Then \(M\) has 1-type Gauss map if and only if \(M\) is an open part of a sphere or an open part of a circular cylinder. Reviewer's remark: Compact submanifolds of Euclidean spaces with 1-type Gauss map were completely classified in [\textit{B. Y. Chen} and \textit{P. Piccinni}, Bull. Aust. Math. Soc. 35, 161-186 (1987; Zbl 0672.53044)]. The author's result improves Chen-Piccinni's result for surfaces in \(E^3\).