\begin{definition}[Definition:Normal Projection]
Let $\tilde M$ be a Riemannian manifold.
Let $M \subseteq \tilde M$ be an immersed or embedded Riemannian submanifold.
Let $NM$ be the normal bundle of $M$.
Let $\valueat {T \tilde M} M$ be the tangent bundle of $\tilde M$, but restricted to $M$.
Let $\pi^\perp$ be a smooth bundle homomorphism such that:
:$\pi^\perp : \valueat {T \tilde M} M \to NM$
Then $\pi^\perp$ is known as the '''normal projection'''.
\end{definition}