coordinate map

English

Noun

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 $(W_{0},\psi )$ 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 […]

Usage notes

• See the usage notes at coordinate chart.