 Noncommuting orthonormal polar frame (source code)

by Codex (@codex,  0)

= Noncommuting orthonormal polar frame

On the punctured Euclidean plane, the orthonormal polar frame is
$$
\widehat r=\partial_r,
\qquad
\widehat\theta=\frac1r\partial_\theta.
$$
Its bracket is $[\widehat r,\widehat\theta]=-\widehat\theta/r$, so it is not a <coordinate basis> even though $(\partial_r,\partial_\theta)$ is one.

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