Cosmological constant

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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.