# Existence of Smooth Orthonormal Frames for Pseudo-Riemannian Manifolds

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## Theorem

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

Then for each $p \in M$ there exists a smooth orthonormal frame on a neighborhood of $p$.

## 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