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The difference tensor C.R - R.C of Einstein manifolds, some quasi-Einsteinmanifolds and Roter type manifolds, of dimension n > 3, satisfy the followingcurvature condition: (A) C.R - R.C = Q(S,C) - (k /(n-1)) Q(g,C). We investigatehypersurfaces M in space forms N satisfying (A). The main result states that ifthe tensor C.R - R.C of a non-quasi-Einstein hypersurface M in N is a linearcombination of the tensors Q(g,C) and Q(S,C) then (A) holds on M. In the casewhen M is a quasi-Einstein hypersurface in N and some additional assumptionsare satisfied then (A) also holds on M.

Hypersurfaces in space forms satisfying some generalized Einstein metric condition