الفهرس 
PrefaceOnly 14 pages are availabe for public view
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Abstract
In chapter one, the introduction of the fundamental geometrical principles on (pseudo-)Riemannian manifolds is covered. As an illustration, we discussed the ideas of connections, curvature, and Ricci curvature. This chapter presents also the definitions of warped product manifolds and doubly warped product manifolds. Generalized Robertson-Walker space-times and a standard static space-times which are usually pictured out as a special case of warped product manifolds are considered. The purpose of chapter two is to investigate how a ρ-Einstein soliton structure on a warped product manifold affects its base and fiber factor manifolds. Firstly, the pertinent properties of ρ- Einstein solitons are provided. Secondly, the numerous necessary and sufficient conditions of a ρ-Einstein soliton warped product manifold to make its factors ρ-Einstein soliton are been examined. On a ρ-Einstein gradient soliton warped product manifold, necessary and sufficient conditions for making its factors ρ- Einstein gradient soliton are presented. ρ-Einstein solitons on warped product manifolds admitting a conformal vector field are also considered. Finally, the structure of ρ-Einstein solitons on some warped product space-times is investigated. In chapter three, warped product mixed generalized quasi- Einstein manifolds is studied. It is shown that a Ricci recurrent mixed generalized quasi-Einstein manifold is a product manifold whose factors are Ricci recurrent. The sufficient conditions for a mixed generalized quasi-Einstein manifold to be a generalized quasi-Einstein manifold is derived. Then, we classify three types of mixed generalized quasi-Einstein warped product manifolds. For example, it is proved that the fiber manifold is Einstein in the first case, generalized quasi-Einstein in the second case and mixed generalized quasi-Einstein in the third case.