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We study minimal surfaces in generic sub-Riemannian manifolds withsub-Riemannian structures of co-rank one. These surfaces can be defined as thecritical points of the so-called {\it horizontal} area functional associated tothe canonical {\it horizontal} area form. We derive the intrinsic equation inthe general case and then consider in greater detail 2-dimensional surfaces incontact manifolds of dimension 3. We show that in this case minimal surfacesare projections of a special class of 2-dimensional surfaces in the horizontalspherical bundle over the base manifold. Generic singularities of minimalsurfaces turn out the singularities of this projection, and we give a completelocal classification of them. We illustrate our results by examples in theHeisenberg group and the group of roto-translations

Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the (2,3) case