Einstein manifold

An Einstein manifold is a Riemannian manifold \((M, g)\) where the Ricci curvature is proportional to the metric tensor \(g\). Mathematically, this relationship can be expressed as: \[ \text{Ric}(g) = \lambda g \] where \(\text{Ric}(g)\) is the Ricci curvature tensor and \(\lambda\) is a constant, often referred to as the "Einstein constant.