  In the differential geometry of certain F-structures, the role of W-curvature
tensor is very well known. A detailed study of this tensor has been made on the
spacetime of general relativity. The spacetimes satisfying Einstein field
equations with vanishing W-tensor have been considered and the existence of
Killing and conformal Killing vector fields has been established. Perfect fluid
spacetimes with vanishing W-tensor have also been considered. The divergence of
W-tensor is studied in detail and it is seen, among other results, that a
perfect fluid spacetime with conserved W-tensor represents either an Einstein
space or a Friedmann-Robertson-Walker cosmological model.
