Hello-

Does anyone know of a reference which describes what the
Riemann curvature and the Einstein equations look like when
considering the embedding diagram of the space-time in higher
dimensions? In other words, if someone were to describe the shape of
the manifold in a higher dimensional space, could one calculate the
curvature and solve the evolution without going to the lower
dimensional (the dimension of the space-time) metric first.

thanks
-J