msv

I have the following problem:

Let $S$ be a smooth oriented surface with unit normal $n$ in the
Euclidean three dimensional space $E$ and let $B$ the second
fundamental tensor on it (Weingarten map). Suppose that a smooth
one-to-one deformation $f$ is applied to an open region of $E$ which
contains $S$. Is anyone aware of a reference where I could find a
formual which gives $B'$, the second fundamental tensor on the surface
$S'$ which is the image of $S$ under $f$, as a function of $B$ and
the gradients of $f$ computed at each poin of the surface $S$?

Thanks for any help.

Maurizio.