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 $(W_{0}, ψ)$ be a smooth coordinate chart for $P$ , and let $(E_{1}, \dots, E_{n - p})$ be a local orthonormal frame for the normal bundle $N P$ ; 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 ${\hat{W}}_{0} = ψ (W_{0}) \subseteq ℝ^{p}$ , and let $N P |_{W_{0}}$ be the portion of the normal bundle over $W_{0}$ . The coordinate map $ψ$ and frame $(E_{j})$ yield a diffeomorphism ${\hat{W}}_{0} \times ℝ^{n - p} \to N P |_{W_{0}}$ defined by […]