  The Newman-Penrose equations for spacetimes having one spacelike Killing
vector are reduced -- in a geometrically defined "canonical frame'' -- to a
minimal set, and its differential structure is studied. Expressions for the
frame vectors in an arbitrary coordinate basis are given, and
coordinate-independent choices of the metric functions are suggested which make
the components of the Ricci tensor in the direction of the Killing vector
vanish.
