  For an evolution of metrics $(M,g_{t})$ there is a t-smooth family of
embeddings $e_{t}:M\to\mathbb{R}^{N}$ 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.
