Abstract
By embedding the space-time V 4 in a higher-dimensional space M N we can formulate a theory of gravity in which the true dynamical variables are the coordinates η a ( x) ( a = 1,2,…, N) of V 4 with respect to M N . Before constrained by the variational principle, which gives the equations of the four-surface V 4, all the coordinates η a are independent. This enables the canonical formulation of the theory (without additional constraints except for the initial and boundary conditions on η a and ones due to the reparametrization invariance) which is presented here. When expressed in terms of the metric tensor g μ v of the space-time four-surface V 4 the theory reduces to the Einstein general relativity.
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