Originally posted by Mike2
I wonder if there are any theorems between changing curvature of some overall manifold and the equivalence of this to the creation of submanifolds.

what do you mean by "changing"? remember that in GR, time is part of the manifold, so there is no way to say the curvature changes in time in a consistent way.
It seems to me that this would be the missing link between the expanding universe of GR and the particles of String Theory.

the link between string theory and GR is not missing, it is well known: String theory contains GR as a first order approximation.
Perhaps this is also a type of symmetry breaking process.

which symmetry did you have in mind to be broken, and what does this have to do with String theory, GR, submanifolds, or changing curvature?