Continuing previous work, some features of the flat embedding theory of class-1 curved space-time are further discussed. In the two-metric formalism provided by the embedding approach the Gauss tensor obtains as the flat-covariant gradient of a fundamental vector potential. The Einstein tensor is then examined in terms of the Gauss tensor. It is proved that the Einstein tensor is divergence free in flat space-time, i.e. a true Lorentz-covariant conservation law for the Einstein tensor is shown to hold. The form of the Einstein tensor in flat space-time also appears as a canonical energy-momentum tensor of the vector potential. The corresponding Lagrangian density, however, does not provide us with a set of field equations for the fundamental vector potential; indeed, the Euler-Lagrange ''equations'' collapse to a useless identity, while the Lagrangian density has the form of a flat divergence.