coordinatemap (pluralcoordinate maps)

1. (differential geometry)Synonym ofcoordinate chart.
   • 2019 January 2, John M. Lee,Introduction to Riemannian Manifolds (Graduate Texts in Mathematics)‎^[1], Springer,→ISBN,→OCLC, page135:

     Let${\displaystyle (W_0,\psi )}$ be a smooth coordinate chart for${\displaystyle P}$, and let${\displaystyle (E_1,\dots ,E_{n-p})}$ be a local orthonormal frame for the normal bundle${\displaystyle NP}$; by shrinking${\displaystyle W_0}$ if necessary, we can assume that the coordinates and the local frame are defined on the same open subset${\displaystyle W_0\subseteq P}$. Let${\displaystyle {\hat{W}}_0=\psi (W_0)\subseteq {\mathbb{R}}^p}$, and let${\displaystyle NP{|}_{W_0}}$ be the portion of the normal bundle over${\displaystyle W_0}$. Thecoordinate map${\displaystyle \psi }$ and frame${\displaystyle (E_j)}$ yield a diffeomorphism${\displaystyle {\hat{W}}_0\times {\mathbb{R}}^{n-p}\to NP{|}_{W_0}}$ defined by[…]

• See the usage notes atcoordinate chart.

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