Exceptional minimal surfaces whose Gauss images have constant curvature (Q1210374)

Let \(X^ n(c)\) be the simply connected \(n\)-dimensional space form of constant curvature \(c\) and \(M\) be an immersed surface of \(X^ n(c)\). Let \(K\) denote the Gaussian curvature of the metric induced in \(M\) by the Gauss map. If \(c\neq 0\), Obata's Gauss map is considered. The purpose of this paper is to study immersed surfaces of \(X^ n(c)\), having constant \(K\). The possible values of \(K\) are given for a class of minimal surfaces called exceptionals in the case where either \(c=0\) or \(n=6\). Exceptional surfaces were studied by \textit{G. D. Johnson} in Pac. J. Math. 149, 113- 125 (1991; Zbl 0729.53053).