Cosmological constant

Definition

Let $M$ be a manifold equipped with an Einstein metric. Then the cosmological constant of $M$ is defined as the constant of proportionality $\lambda$ for which:

$R_{ij}=\lambda g_{ij}$

where $R$ denotes the Ricci curvature tensor.

Equivalently the cosmological constant for an Einstein metric can be defined as the Ricci curvature associated with any one-dimensional subspcae of the tangent space.