An example of non-embeddability of the Ricci flow.

For an evolution of metrics (M , g t) there is a t-smooth family of embeddings e t : M → R N inducing g t , but in general there is no family of embeddings extending a given initial embedding e 0 . We give an example of this phenomenon when g t is the evolution of g 0 under the Ricci flow. We show that there are embeddings e 0 inducing g 0 which do not admit of t-smooth extensions to e t inducing g t for any t > 0 . We also find hypersurfaces of dim > 2 that will not remain a hypersurface under Ricci flow for any positive time. [ABSTRACT FROM AUTHOR]