Abstract

It is pointed out that every generic - in a sense to be made precise in section 2 - solution to an arbitrary equation describing pseudo-spherical surfaces (or, equivalently, an arbitrary equation which is the integrability condition of a sl(2, R)-valued linear problem) determines pseudo-Riemannian surfaces of constant scalar curvature, and therefore, classical solutions to the Jackiw-Teitelboim field equations for two-dimensional gravity. In particular, this observation explains why some standard soliton equations appear in this theory.