  The properties of some locally rotationally symmetric (LRS) perfect fluid
space-times are examined in order to demonstrate the usage of the description
of geometries in terms of the Riemann tensor and a finite number of its
covariant derivatives for finding solutions to Einstein's field equations. A
new method is introduced, which makes it possible to choose the coordinates at
any stage of the calculations. Three classes are examined, one with fluid
rotation, one with spatial twist in the preferred direction and the space-time
homogeneous models. It is also shown that there are no LRS space-times with
dependence on one null coordinate. Using an extension of the method, we find
the full metric in terms of curvature quantities for the first two classes.
