Constraints of the Teleparallel Equivalent of General Relativity in a gauge

We consider a specific Hamiltonian formulation of the Teleparallel Equivalent of General Relativity, where the canonical variables are expressed by means of differential forms. We show that some position'' variables of this formulation can be always gauge-transformed to zero. In this gauge the constraints of the theory become simpler, and the other position’’ variables acquire a nice geometric interpretation that allows for an alternative, clearer form of the constraints. Based on these results we derive some exact solutions to the constraints.