Wente torus

In differential geometry, a Wente torus is an immersed torus in

3

of constant mean curvature, discovered by Henry C. Wente (1986).

It is a counterexample to the conjecture of Heinz Hopf that every closed, compact, constant-mean-curvature surface is a sphere (though this is true if the surface is embedded).

There are similar examples known for every positive genus.