\begin{definition}[Definition:Metric Induced by Smooth Immersion]
Let $\struct {\tilde M, \tilde g}$, $\struct {M, g}$ be Riemannian manifolds.
Let $F : M \to \tilde M$ be a smooth immersion.
Suppose, the metric $g$ is such that $g = F^* \tilde g$.
Then $g$ is called the '''metric induced by $F$'''.
\end{definition}