Constant mean curvature tori with spherical curvature lines in noneuclidean geometry (Q1822770)

Tori with constant mean curvature are found in the three dimensional standard sphere and in hyperbolic space all of whose curvature lines are all spherical. In Euclidean space, constant mean curvature tori were first found by \textit{H. C. Wente} [Pac. J. Math. 121, 193-243 (1986; Zbl 0586.53003)], see also \textit{U. Abresch} [J. Reine Angew. Math. 374, 169- 192 (1987; Zbl 0597.53003)], \textit{U. Pinkall} and \textit{I. Sterling} [Ann. Math., II. Ser. 130, 407-451 (1989)], and the author [Geom. Dedicata 23, 187-213 (1987; Zbl 0615.53050)].