coordinate map

coordinate map (plural coordinate maps)

1. (differential geometry) Synonym of coordinate chart.
   • 2019 January 2, John M. Lee, Introduction to Riemannian Manifolds (Graduate Texts in Mathematics)‎, Springer, →ISBN, →OCLC, page 135:

     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 ${\displaystyle NP\vert _{W_{0}}}$ be the portion of the normal bundle over ${\displaystyle W_{0}}$. The coordinate map ${\displaystyle \psi }$ and frame ${\displaystyle (E_{j})}$ yield a diffeomorphism ${\displaystyle {\hat {W}}_{0}\times \mathbb {R} ^{n-p}\rightarrow NP\vert _{W_{0}}}$ defined by […]

• See the usage notes at coordinate chart.