  A subclassification of stationary spacetimes, endowed with one timelike and
one spacelike Killing vectors, i.e., Petrov $G{_2}I$ on $T_2$ spaces, is
proposed. Special attention deserves the Collison's theorem [1] and the branch
of metrics circularly cyclicly (axially) symmetric possessing additionally the
conformal flatness property reported by Garcia and Campuzano [2].
