  The main object of the present paper is to study the geometric properties of
a generalized Roter type semi-Riemannian manifold, which arose in the way of
generalization to find the form of the Riemann-Christoffel curvature tensor
$R$. Again for a particular curvature restriction on $R$ and the Ricci tensor
$S$ there arise two structures, e. g., local symmetry ($\nabla R = 0$) and
Ricci symmetry ($\nabla S = 0$); semisymmetry($R\cdot R =0$) and Ricci
semisymmetry ($R\cdot S =0$) etc. In differential geometry there is a very
natural question about the equivalency of these two structures. In this context
it is shown that generalized Roter type condition is a sufficient condition for
various important second order restrictions. Some generalizations of Einstein
manifolds are also presented here. Finally the proper existence of both type of
manifolds are ensured by some suitable examples.
