take a Riemannian manifold $(\overline{M}, \overline{g})$ and a time dependent family of smooth embeddings $\phi( \cdot , t)$ of a hypersurface $(M,g)$ immersed via the inclusion mapoing $j: M \rightarrow \overline{M}$. For each $p \in M$ denote by $F_{t}(p): T_{p}M \rightarrow T_{\phi_{t}(p)}\overline{M}$ the differential of $\phi(, t)$.