Let $M$ be complex manifold which is Kobayashi hyperbolic. Let $N$ be a submanifold of $M$ obtained as the zeroes of an analytic submersion $f : M \rightarrow R$, $R$ complex manifold.
Question : what can be said about the restriction of the Kobayashi metric of $M$ to $N$ ? Is it the Kobayashi metric of $N$ ? Does it change anything if we know $\dim_{\mathbb{C}} N=1$ ?