A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity
vector field, 2) null divergence of the Weyl tensor, is a generalised
Robertson-Walker space-time with Einstein fiber. Condition 1) is verified
whenever pressure and energy density are related by an equation of state. The
contraction of the Weyl tensor with the velocity vector field is zero.
Conversely, a generalized Robertson-Walker space-time with null divergence of
the Weyl tensor is a perfect-fluid space-time.Comment: 7 pages. Misprint corrected in Sect II
