Three-Dimensional Matrix Superpotentials - Karadzhov, Yu. A. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We consider a special case for curves in two-, three-, and four-dimensional Euclidean spaces and obtain a necessary and sufficient condition for the tensor product surfaces of the planar unit circle centered at the origin and these curves to have a harmonic Gauss map. We present а classification of matrix superpotentials that correspond to exactly solvable systems of Schrodinger equations. Superpotentials of the following form are considered: W_k = kQ + P 1k, where k is a parameter and P, Q and R are Hermitian matrices that depend on a variable x. The list of three-dimensional matrix superpotentials is explicitly presented.