Isothermic surfaces and Hopf cylinders (Q1866593)

In 1985 [Invent. Math. 81, 379--386 (1985; Zbl 0585.53051)] \textit{U. Pinkall} introduced Hopf cylinders in the three-dimensional unit sphere \(S^3\subset\mathbb{R}^4\) which are inverse images of spherical curves in the two-dimensional sphere \(S^2\subset\mathbb{R}^3\) by means of the Hopf map. Based on the work of Pinkall, characterizations of spherical curves are given whose corresponding Hopf cylinders are isothermic surfaces in the three-dimensional sphere. Comparing these characterizations with results of J. Langer and D. A. Singer about elastic spherical curves the authors determine all isothermic Willmore Hopf tori.