Necessary and Sufficient Condition for Hypersurface in Oriented Riemannian Manifold to be Orientable

Theorem
Let $\struct {\tilde M, \tilde g}$ be an oriented Riemannian manifold.

Let $M$ be a hypersurface in $\tilde M$.

Let $g$ be the induced metric on $M$.

Then $M$ is orientable there exists a unit global normal vector $N$ for $M$.