  Using a strongly covariant formalism given by Carter for the deformations
dynamics of p-branes in a curved background and a covariant and gauge invariant
geometric structure constructed on the corresponding Witten's phase space, we
identify the canonical variables for Dirac-Nambu-Goto [DNG] and Gauss-Bonnet
[GB] system in string theory. Future extensions of the present results are
outlined.
