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 (with appropriate metric tensors) can be used in the stated classes of Riemannian and pseudo-Riemannian surfaces:

Surface Class	Surface	Charts
n-spheres	n-sphere Sn	Hopf chart Hyperspherical coordinates
	Sphere S2	Spherical coordinates Stereographic chart Central projection chart Axial projection chart Mercator chart
	3-sphere S3	Polar chart Stereographic chart Mercator chart
Euclidean spaces	n-dimensional Euclidean space En	Cartesian chart
	Euclidean plane E2	Bipolar coordinates Biangular coordinates Two-center bipolar coordinates
	Euclidean space E3	Polar spherical chart Cylindrical chart Elliptical cylindrical, hyperbolic cylindrical, parabolic cylindrical charts Parabolic chart Hyperbolic chart Prolate spheroidal chart (rational and trigonometric forms) Oblate spheroidal chart (rational and trigonometric forms) Toroidal chart
Hyperbolic spaces	n-dimensional hyperbolic space Hn	Upper half-space chart (Poincaré model) Hopf chart Central projection chart (Klein model)
	Hyperbolic plane H2	Polar chart Stereographic chart (Poincaré model)
Embedded surfaces	Embedded in E3	Monge chart[1]
Minimal surfaces	Minimal surfaces	Asymptotic chart
Lorentzian manifolds	De Sitter space dSn	Static chart
	Anti-de Sitter space AdSn	Half-space chart

See also

• Coordinate chart
• Coordinate system
• Metric tensor
• List of mathematics lists, particularly:
  • List of multivariable calculus topics
  • List of Fourier analysis topics
  • List of differential geometry topics