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 $\valueat {T \tilde M} M$.

Proof

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Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Pseudo-Riemannian Metrics