Die EINSTEIN-Gruppe und die Symmetrie-Gruppen der Gravitationstheorie

The transformations x^?α = x^?α(x^β, g_μn?) in the function space of the g_μn?(x^λ) are corresponding to the coordinate transformations x^α = x^α(x^β) with some non-covariant conditions on the g_μn?(x^λ). Therefore, the transformations in the function space are corresponding to subgroups of the EINSTEIN group. The conditions for the g_μn? may be given in the space- time V₄ or on submanifolds (points, curves, surfaces and hypersurfaces) of the V₄. – A special case of the last problem is given by the CAUCHY conditions or by the DIRAC constraints for a special choice of the coordinates on a CAUCHY hypersurface x⁰ = 0. Then, the transformations x^?α = x^?α(x^l, g_rs, p^mn) in the phase space are EINSTEIN transformations preserving the synchronicity for x⁰ → 0.