Let $f:X\rightarrow C$ be a morphism, where $C$ is a smooth curve, and let $\Omega_f$ be the sheaf of relative differentials.

For $t\in C$ let $i_t:X_t = f^{-1}(t)\rightarrow X$ be the inclusion of the fiber of $f$ over $t$. Does there exist an isomorphism $i_t^{*}\Omega_f \cong \Omega_{X_t}$ ?