  This is a shortened version of an invited talk at the XIII International
Workshop "Lie Theory and its Applications in Physics", June 17-23, Varna,
Bulgaria. A covariant canonical gauge theory of gravity free from torsion is
studied. Using a metric conjugate momentum and a connection conjugate momentum,
which takes the form of the Riemann tensor, a gauge theory of gravity is
formulated, with form-invariant Hamiltonian. By the metric conjugate momenta, a
correspondence between the Affine-Palatini formalism and the metric formalism
is established. For, when the dynamical gravitational Hamiltonian
$\tilde{H}_{Dyn}$ does not depend on the metric conjugate momenta, a metric
compatibility is obtained from the equation of motions, and the equations of
motion correspond to the solution is the metric formalism.
