2-DIMENSIONAL HIGHER-DERIVATIVE QUANTUM-GRAVITY WITH CONSTANT-CURVATURE CONSTRAINT

The quantization of the two-dimensional R2-gravity coupled with confor mal matters under the constraint of constant curvature is discussed. T he partition function for this system is found for arbitrary genus. It is shown that no critical dimension exists as in the case of the Jack iw-Teitelboim model. In the case of the R2-gravity coupled with fermio ns described by the Gross-Neveu model a semiclassical solution is cons tructed which represents a modified version of the CGHS-Witten black h ole.