In the book "Kinetic theory in the expanding Universe" (J. Bernstein, 1988, Camb. Univ. Press), it was stated that
"for nonstationary Robertson-Walker matrixes [sic] there is no spacelike Killing vector."
(page 6, footnote.)
But we know this is not true, since one can see that the generators of spatial translations/rotations are manifestly space-like. (For example, see R. Maartens and S.D. Maharaj, Class. Quantum Grav. 3 (1986) 1005-1011, equation (1.7)).
Was the author of the book wrong, or was it a slip of the hand, where "spacelike" should have been "timelike" (but that would amount to tautology anyway, since "nonstationary" is defined in terms of the absence of a time-like Killing vector).