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Einstein manifold
In
differential geometry
and
mathematical physics
, an
Einstein manifold
is a
Riemannian
or
pseudo-Riemannian 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 the dimension, as well as the signature, of the metric can be arbitrary, unlike the four-dimensional
Lorentzian manifolds
usually studied in
general relativity
.
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