Constructions of almost complex 2-tori of type (III) in the nearly Kahler 6-sphere

In this paper, we give a machinery method of constructing almost complex curve of type (III) in the nearly Kahler 6-sphere. As application, a first non-trivial example of almost complex 2-tori of type (III) will be described in terms of the Jacobi elliptic functions. In the final section, a general solution of such tori will be described in terms of the Prym-theta functions using the known results from the integrable system theory.