  Rigidly rotating stationary matter in general relativity has been
investigated by Kramer by the Ernst coordinate method. A weakness of this
approach is that the Ernst potential does not exist for differential rotation.
We now generalize the techniques by the use of a nonholonomic and nonrigid
frame. We apply these techniques for differentially rotating perfect fluids. We
construct a complex analytic tensor, characterizing the class of matter states
in which both the interior Schwarzschild and the Kerr solution are contained.
We derive consistency relations for this class of perfect fluids. We
investigate incompressible fluids characterized by these tensors.
