On almost Pseudo Ricci symmetric manifolds

The main concern of this thesis is to investigate an n−dimensional almost pseudo Ricci symmetric manifold (M;g) whose Ricci tensor S satisfies the condition (∇ZS)(X,Y) = [A(Z)+ B(Z)]S(X,Y)+ A(X)S(Y,Z)+ A(Y)S(X,Z) where A and B are two non-zero 1−forms and ∇ denotes the operator of the covariant differentiation with respect to the metric g. Such a manifold is called almost pseudo Ricci symmetric manifold and denoted by A(PRS)n. In the first Chapter, some significant definitions and notions.In the second Chapter, a historical overview of the important role of symmetric spaces in differential geometry is given.In the third Chapter, an almost pseudo Ricci symmetric manifold admitting W2−Ricci tensor has been analyzed. The last Chapter is concerned with an almost pseudo Ricci symmetric spacetime. Under some conditions, we determine the properties of this spacetime.