Coverings and integrability of the Gauss-Mainardi-Codazzi equations
  Using covering theory approach (zero-curvature representations with the gauge group SL2), we insert the spectral parameter into the Gauss-Mainardi-Codazzi equations in Tchebycheff and geodesic coordinates. For each choice, four integrable systems are obtained. 
Joseph Krasil'shchik and Michal Marvan