Abstract
Stationary axisymmetric perfect fluid spacetimes are investigated using the curvature description of geometries. We formulate the equations in terms of components of the Riemann tensor and the Ricci rotation coefficients in a comoving Lorentz tetrad. It is shown that the only incompressible axistationary magnetic perfect fluid is the interior Schwarzschild solution. Further, we find that all rigidly rotating axistationary fluids with magnetic Weyl tensor have local rotational symmetry. Rigidly rotating fluid spacetimes with purely electric or purely magnetic Weyl tensor are shown to be of Petrov type D.
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