Wente tori

Historically the first immersed constant mean curvature tori were constructed by H. Wente in 1984 [86] by analytical methods. A short time later U. Abresch simplified this construction. He remarked that Wente tori should possess planar curvature lines and thus studied all CMC surfaces with planar curvature lines. It leads to an overdetermined system of equations which can be solved by quadratures using elliptic integrals. And U. Abresch showed that some of the obtained immersed surfaces do close up, giving CMC tori [1] (see also [87]).