Existence of Smooth Orthonormal Frames for Pseudo-Riemannian Manifolds

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