\begin{definition}[Definition:Isometric Immersion]
Let $\struct {M, g}$, $\struct {\tilde M, \tilde g}$ be Riemannian manifolds.
Let $F : M \to \tilde M$ be an immersion such that $F^* \tilde g = g$.
Then $F$ is called an '''isometric immersion'''.
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\end{definition}