Die E INSTEIN ‐Gruppe und die Symmetrie‐Gruppen der Gravitationstheorie

The transformations x −α = x −α ( x β , g μn̈ ) in the function space of the g μn̈ ( x λ ) are corresponding to the coordinate transformations x α = x α ( x β ) with some non‐covariant conditions on the g μn̈ ( x λ ). Therefore, the transformations in the function space are corresponding to subgroups of the E INSTEIN group. The conditions for the g μn̈ may be given in the space‐ time V 4 or on submanifolds (points, curves, surfaces and hypersurfaces) of the V 4 . – A special case of the last problem is given by the C AUCHY conditions or by the D IRAC constraints for a special choice of the coordinates on a C AUCHY hypersurface x 0 = 0. Then, the transformations x −α = x −α ( x l , g rs , p mn ) in the phase space are E INSTEIN transformations preserving the synchronicity for x 0 → 0.