CANONICAL VIELBEIN FORMS OF D=3 AND D=4 GRAVITY

We compare, in both D=3 and D=4, two vielbein canonical formulations o f gravity: that of Deser and Isham which starts with the metric replac ed by vielbeins in the ADM action, and that starting directly from fir st order vielbein action, and compute the functional that generates th e canonical transformation between these two formulations. In D=3, the generator thus exhibits the inherent simplicity of the Einstein actio n, starting from the DI form (which is as complicated as in D=4). In D =4, however, the same procedure, while leads to a somewhat different f ormulation from the existing ones, does not result in miraculous simpl ifications.