The Multidimensional Darboux Transformation
  A generalization of the classical one-dimensional Darboux transformation to arbitrary n-dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The classical two-dimensional Moutard transformation is also generalized to non-compact oriented Riemannian manifolds of dimension n greater than one. New examples of quasi-exactly solvable multidimensional matrix Schr\"odinger operators on curved manifolds are obtained by applying the above results. 
Artemio Gonz\'alez-L\'opez (Dept. F\'isica Te\'orica II, U.   Complutense, Madrid) and Niky Kamran (The Fields Institute, To...