I have an m-dimensional riemannian manifold M and an n-dimensional submanifold N that is given by $N = f^{-1}(0)$, where $f: M \longrightarrow \mathbb{R}^{m-n}$ ($0$ is supposed to be a regular value of f).
How can I express the second fundamental form of N in terms of f?
\Edit: I forgot to clarify what $f$ is