and quaternionic projective spaces

The problem of constructing harmonic maps of two-spheres into spheres, complex Grassmann manifolds and quaternionic projective spaces is already solved and well under-$\mathrm{s}\mathrm{t}_{\mathrm{o}\mathrm{O}}\mathrm{d}$(see [Ba-W], [B-W], [Cal], $[\mathrm{C}\mathrm{a}2],[\mathrm{w}\mathrm{o}], $ $[\mathrm{W}] $). The next problem is to construct and understand the harmonic maps of two-tori in spheres, complex Grassmann manifolds and quaternionic projective spaces. In contrast with the case of harmonic two-spheres, there is a class of non-conformal harmonic maps for two-tori. For non-conformal harmonic two-tori in compact symmetric space of rank one, a beautiful theory is established by [B-F-P-P], which says that they are obtained by integrating certain commuting Hamiltonian flows. They called the map of this kind a map of finite type. However, the geometrically interesting class of harmonic maps is that of conformal ones. The (weakly) conformal harmonic maps are divided into two subclasses, the class of superminimal ones and the class of non-superminimal ones. The former class is well understood (see [Cal], [Ca2], [Ch], [E-W], [Ba-W]); its members are projections of horizontal holomorphic curves in certain generalized flag manifolds, which are twistor spaces of the underlying symmetric space. The latter class was recently treate