Axistationary perfect fluids -- a tetrad approach

Stationary axisymmetric perfect fluid space-times are investigated using the curvature description of geometries. Attention is focused on space-times with a vanishing electric part of the Weyl tensor. It is shown that the only incompressible axistationary magnetic perfect fluid is the interior Schwarzschild solution. The existence of a rigidly rotating perfect fluid, generalizing the interior Schwarzschild metric is proven. Theorems are stated on Petrov types and electric/magnetic Weyl tensors.