  Both the Einstein-Hilbert action and the Einstein equations are discussed
under the absolute vierbein formalism. Taking advantage of this form, we prove
that the "kinetic energy" term, i.e., the quadratic term of time derivative
term, in the Lagrangian of the Einstein-Hilbert action is non-positive
definitive. And then, we present two groups of coordinate conditions that lead
to positive definitive kinetic energy term in the Lagrangian, as well as the
corresponding actions with positive definitive kinetic energy term,
respectively. Based on the ADM decomposition, the Hamiltonian representation
and canonical quantization of general relativity taking advantage of the
actions with positive definitive kinetic energy term are discussed; especially,
the Hamiltonian constraints with positive definitive kinetic energy term are
given, respectively. Finally, we present a group of gauge conditions such that
there is not any second time derivative term in the ten Einstein equations.
