
It is possible to describe the gravitational field via a theory of 4d surface embedded into the 10d flat space. For the first time such a model, in which the usual form of action written down in terms of embedding function is used, was considered by T.Regge, C.Teitelboim in 1975. However in such approach the equations of the gravitational field are more general than Einstein's equations, i.e. the theory is not equivalent to General Relativity. To achieve the equivalence it is proposed to modify the theory by additional imposition of constraints under the construction of canonical formalism. Finally the theory with eightparametric gauge symmetry is obtained. This theory turns out to be equivalent to Einstein's General Relativity if we partially fix the gauge or redefine the metric taking for it an expression which is invariant under additional gauge transformations. The action for such a theory is constructed.
