einstein manifolds from a physical and mathematical view point

In this paper, we introduce einstein’s manifold theory from a mathematical and physical viewpoint. we present some obstructions for a manifold to be equipped with the structure of an einstein manifold. we discuss the hamiltonian approach to einstein manifold theory and the chirality of the lie algebra of an einstein lie group. we also discuss einstein’s structure on non-compact manifolds and present some partial results on einstein’s structure on the tangent bundle.