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)‎^[1], 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.