The multidimensional Darboux transformation
Abstract
A generalization of the classical onedimensional Darboux transformation to arbitrary ndimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The classical twodimensional Moutard transformation is also generalized to noncompact oriented Riemannian manifolds of dimension n ≥ 2. New examples of quasiexactly solvable multidimensional matrix Schrödinger operators on curved manifolds are obtained by applying the above results.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 July 1998
 DOI:
 10.1016/S03930440(97)000442
 arXiv:
 arXiv:hepth/9612100
 Bibcode:
 1998JGP....26..202G
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Differential Geometry;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 plain TeX, 29 pages. Auxiliary file Darboux.ref and macros file ao.tex