  Let G/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle
T(G/H) contains a maximal G-invariant neighbourhood of the zero section where
the adapted complex structure exists. Such neighbourhood is endowed with a
canonical G-invariant pseudo-Kaehler metric of the same signature as the metric
on G/H. We use the polar map from T(G/H) to the complexified symmetric space
G^C/H^C to define a G-invariant pseudo-Kaehler metric on distinguished
G-invariant domains in G^C/H^C or on coverings of principal orbit strata in
G^C/H^C.
