On closed Weingarten surfaces (Q814802)

In the paper under review, the authors investigate closed Weingarten surfaces in Euclidean \(3\)-space satisfying some functional relations of the form \(\kappa=F(\lambda)\), where \(\kappa\) and \(\lambda\) are the principal curvatures. Some new examples of such surfaces from the class of surfaces of revolution are found. In particular, the authors obtain examples of analytic closed surfaces of genus zero for \(F(\lambda)=c{\lambda}^{2n+1}\), \(n \in \mathbb{N}\). This generalizes well-known results of \textit{H.~Hopf} [Math. Nachr. 4, 232--249 (1951; Zbl 0042.15703)].