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The properties of some locally rotationally symmetric (LRS) perfect fluidspace-times are examined in order to demonstrate the usage of the descriptionof geometries in terms of the Riemann tensor and a finite number of itscovariant derivatives for finding solutions to Einstein's field equations. Anew method is introduced, which makes it possible to choose the coordinates atany stage of the calculations. Three classes are examined, one with fluidrotation, one with spatial twist in the preferred direction and the space-timehomogeneous models. It is also shown that there are no LRS space-times withdependence on one null coordinate. Using an extension of the method, we findthe full metric in terms of curvature quantities for the first two classes.Comment: 24 pages, LaTeX (uses ioplppt

Invariant construction of solutions to Einstein's field equations - LRS perfect fluids I