Existence of Normal Bundle to Pseudo-Riemannian Submanifold

Theorem
Let $\struct {\tilde M, \tilde g}$ be a pseudo-Riemannian manifold.

Let $M \subseteq \tilde M$ be an embedded pseudo-Riemannian or Riemannian submanifold.

Let $NM$ be the normal bundle of $M$.

Then $NM$ is a smooth vector subbundle of $\valueat {T \tilde M} M$.