List of coordinate charts

This article contains a non-exhaustive list of coordinate charts for Riemannian manifolds and pseudo-Riemannian manifolds. Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics.

Charts for Riemannian and pseudo-Riemannian surfaces

The following charts can be used in the stated classes of Riemannian and pseudo-Riemannian surfaces:

Surface Class	Surface	Charts
[N-sphere\|]-spheres	'-sphere S'ⁿ	Hopf chart Hyperspherical coordinates
[N-sphere\|]-spheres	Sphere S²	Spherical coordinates Stereographic chart Central projection chart Axial projection chart Mercator chart
[N-sphere\|]-spheres	3-sphere S³	Polar chart Stereographic chart Mercator chart
Euclidean spaces	'-dimensional Euclidean space E'ⁿ	Cartesian chart
Euclidean spaces	Euclidean plane E²	Bipolar coordinates Biangular coordinates Two-center [bipolar coordinates]
Euclidean spaces	Euclidean space E³	Polar spherical chart Cylindrical chart Elliptical cylindrical, hyperbolic cylindrical, parabolic cylindrical charts Parabolic chart Hyperbolic chart Prolate spheroidal chart Oblate spheroidal chart Toroidal chart
Hyperbolic spaces	'-dimensional hyperbolic space H'''ⁿ	Upper half-space chart Hopf chart Central projection chart
Hyperbolic spaces	Hyperbolic plane H²	Polar chart Stereographic chart
Embedded surfaces	Embedded in E³	Monge chart
Minimal surfaces	Minimal surfaces	Asymptotic chart
Lorentzian manifolds	De Sitter space dSn	Static chart
Lorentzian manifolds	Anti-de Sitter space AdS_n	Half-space chart