einstein manifolds from a mathematical and physical point of view

In this paper we introduce einstein manifold theory from a mathematical and physical view point.we present some obstructions for a manifold to be equipped with the structure of an einstein manifold. we discuss about hamiltonian approach to the einstein manifold theory and also the chirality of the lie algebra of an einstein lie group. some partial results on einstein structure on the tangent bundle are provided. the einstein structure on a manifold is examined via comparison of isometric group of the manifold with the group of all diffeomorphisms preserving the ricci tensor