  The difference tensor C.R - R.C of Einstein manifolds, some quasi-Einstein
manifolds and Roter type manifolds, of dimension n > 3, satisfy the following
curvature condition: (A) C.R - R.C = Q(S,C) - (k /(n-1)) Q(g,C). We investigate
hypersurfaces M in space forms N satisfying (A). The main result states that if
the tensor C.R - R.C of a non-quasi-Einstein hypersurface M in N is a linear
combination of the tensors Q(g,C) and Q(S,C) then (A) holds on M. In the case
when M is a quasi-Einstein hypersurface in N and some additional assumptions
are satisfied then (A) also holds on M.
