In this paper, we study the (1+1)-dimensional Schrödinger-Maxwell-Bloch equation (NLS-MBE) which is integrable by the Inverse Scattering Method. Its Lax pair is presented. We apply methods of the theory of integrable systems to the geometry of surfaces immersed in Euclidean spaces. Using Sym-Tafel formula we construct the first and second fundamental forms, the Gaussian (total) curvature, mean curvature and Christoffel symbols for the NLS-MBE.
Digital Object Identifier: 10.7546/giq-21-2020-320-327