coordinate map

plural coordinate maps

1. differential geometrySynonym of coordinate chart.

   1 more example

   Let (W#95;0,#92;psi) be a smooth coordinate chart for P, and let (E#95;1,#92;dots,E#95;#123;n-p#125;) be a local orthonormal frame for the normal bundle NP; by shrinking W#95;0 if necessary, we can assume that the coordinates and the local frame are defined on the same open subset W#95;0#92;subseteqP. Let #92;hat#123;W#125;#95;0#61;#92;psi(W#95;0)#92;subseteq#92;mathbb#123;R#125;ᵖ, and let NP#92;vert#95;#123;W#95;0#125; be the portion of the normal bundle over W#95;0. The coordinate map #92;psi and frame (E#95;j) yield a diffeomorphism #92;hat#123;W#125;#95;0#92;times#92;mathbb#123;R#125;#123;n-p#125;#92;rightarrowNP#92;vert#95;#123;W#95;0#125; defined by[…]

   2019 January 2, John M. Lee, Introduction to Riemannian Manifolds (Graduate Texts in Mathematics), Springer, →ISBN, →OCLC, page 135

   Synonyms: coordinate chart