  We study the problem of construction of explicit isometric embeddings of
(pseudo)-Riemannian manifolds. We discuss the method which is based in the idea
that the exterior symmetry of the embedded surface and the interior symmetry of
the metric on it must be the same. In case of high enough symmetry of the
metric such method allows to transform the metric inducedness condition, which
is the one to be solved in order to construct an embedding, into a system of
ODEs. It turns out that this method can be generalized to allow the surface to
have lower symmetry as long as the above simplification occurs. This
generalization can be of use in the construction of embeddings for metrics
whose symmetry group is hard to analyze, as well for the construction of
isometrically deformed (bended) surface. We give some examples of application
of this method. In particular, we construct the embedding of spatially-flat
Friedmann model and isometric bendings of sphere, 3-sphere and squashed AdS
universe, which is connected to the Godel universe.
