coordinate map

English

coordinate map (plural coordinate maps)

(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 $(W_{0},\psi )$ be a smooth coordinate chart for $P$ , and let $(E_{1},\dots ,E_{n-p})$ be a local orthonormal frame for the normal bundle $NP$ ; by shrinking $W_{0}$ if necessary, we can assume that the coordinates and the local frame are defined on the same open subset $W_{0}\subseteq P$ . Let ${\hat {W}}_{0}=\psi (W_{0})\subseteq \mathbb {R} ^{p}$ , and let $NP\vert _{W_{0}}$ be the portion of the normal bundle over $W_{0}$ . The coordinate map $\psi$ and frame $(E_{j})$ yield a diffeomorphism ${\hat {W}}_{0}\times \mathbb {R} ^{n-p}\rightarrow NP\vert _{W_{0}}$ defined by […]