: Mathématiques: Einstein manifold

topology > algebraic topology > manifold > differentiable manifold > Einstein manifold

geometry > topological space > manifold > differentiable manifold > Einstein manifold

geometry > differential geometry > differentiable manifold > Einstein manifold

topology > differential topology > differentiable manifold > Einstein manifold

mathematical physics > Einstein manifold

Einstein manifold

In differential geometry and mathematical physics, an Einstein manifold is a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor is proportional to the metric. They are named after Albert Einstein because this condition is equivalent to saying that the metric is a solution of the vacuum Einstein field equations (with cosmological constant), although both the dimension and the signature of the metric can be arbitrary, thus not being restricted to Lorentzian manifolds (including the four-dimensional Lorentzian manifolds usually studied in general relativity). Einstein manifolds in four Euclidean dimensions are studied as gravitational instantons.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Einstein_manifold)

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