Discrete analogs of the Darboux-Egoroff metrics

Akhmetshin, A. A.; Krichever, I. M.; Volvovski, Y. S.

Discrete analogs of the Darboux-Egoroff metrics

Authors

Akhmetshin, A. A.

Krichever, I. M.

Volvovski, Y. S.

Description

Discrete analogs of the Darboux-Egoroff metrics are considered. It is shown that the corresponding lattices in the Euclidean space are described by discrete analogs of the Lame equations. It is proved that up to a gauge transformation these equations are necessary and sufficient for discrete analogs of rotation coefficients to exist. Explicit examples of the Darboux-Egoroff lattices are constructed by means of algebro-geometric methods.
27 pages, LaTeX 2e