Heterotic (2,1) supergravity in two dimensions

We consider a two-dimensional heterotic supergravity theory which exhibits extended N=2 local supersymmetry among the left-moving degrees of freedom and unextended N=1 local supersymmetry - together with a U(1) gauge symmetry - among the right-moving ones. We derive the corresponding super-Liouville action - i.e. the effective action for the supergravity degrees of freedom in the superconformal gauge - and the associated scaling properties. We apply these results to the construction of non-critical heterotic N=(2,1) string models, corresponding to the propagation in kaehlerian target spaces, with a time-dependent background. (orig.)