  The Einstein equations (EE) are certain conditions on the Riemann tensor on
the real Minkowski space M. In the twistor picture, after complexification and
compactification M becomes the Grassmannian $Gr_{2}^{4}$ of 2-dimensional
subspaces in the 4-dimensional complex one. Here we answer for which of the
classical domains considered as manifolds with G-structure it is possible to
impose conditions similar in some sense to EE. The above investigation has its
counterpart on superdomains: an analog of the Riemann tensor is defined for any
supermanifold with G-structure with any Lie supergroup G. We also derive
similar analogues of EE on supermanifolds. Our analogs of EE are not what
physicists consider as SUGRA (supergravity), for SUGRA see \cite{GL4,LP2}.

Differential Geometry