  Generalized Roter type manifold is a generalization of conformally flat
manifold as well as Roter type manifold, which gives rise the form of the
curvature tensor in terms of algebraic combinations of the fundamental metric
tensor and Ricci tensors upto level 2. The object of the present paper is to
investigate the characterizations of a warped product manifold to be
generalized Roter-type. We also present an example of a warped product manifold
which is generalized Roter type but not Roter type, and also an example of a
warped product manifold which is Roter type but not conformally flat. These
examples ensure the proper existence of such notions.

Differential Geometry