Minimal tori in the five-dimensional sphere in $\mathbb C^3$

The class of surfaces that have a certain property (called complexnormal) in the five-dimensional sphere in $\mathbb C^3$ is considered. It is shown that the minimal tori in this class are described by the equation $u_{z\overline{z}}=e^{-2u}-e^u$, which can be integrated by the inverse scattering method. The construction of finite-gap minimal tori that are complexnormal in the five-dimensional sphere in $\mathbb C^3$ is described.