Three-dimensional Background Field Gravity: A Hamilton-Jacobi analysis

We analyse the constraint structure of the Background Field model for three dimensional gravity including a cosmological term via the Hamilton-Jacobi formalism. We find the complete set of involutive Hamiltonians that assures the integrability of the system and calculate the characteristic equations of the system. We established the equivalence between these equations and the field equations and also obtain the generators of canonical and gauge transformations.