Definition:Orthonormal Frame
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Definition
Let $M$ be a Riemannian manifold.
Let $U \subseteq M$ be an open set.
Let $p \in M$ be a point.
Let $T_p M$ be a tangent space of $M$ at $p$.
Let $\tuple {E_i}$ be the local frame for $M$ on $U$.
Suppose for each $p \in U$ the vectors $\bigvalueat {E_i} p$ are an orthonormal basis for $T_p M$.
Then $\tuple {E_i}$ is said to be an orthonormal frame.
Also see
- Results about orthonormal frames can be found here.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Definitions