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 ClassSurfaceCharts-spheres-sphere SnHopf chart Hyperspherical coordinatesSphere S2Spherical coordinates Stereographic chart Central projection chart Axial projection chart Mercator chart3-sphere S3Polar chart Stereographic chart Mercator chartEuclidean spaces-dimensional Euclidean space EnCartesian chartEuclidean plane E2Bipolar coordinates Biangular coordinates Two-center bipolar coordinatesEuclidean space E3Polar 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 chartHyperbolic spaces-dimensional hyperbolic space HnUpper half-space chart (Poincaré model) Hopf chart Central projection chart (Klein model)Hyperbolic plane H2Polar chart Stereographic chart (Poincaré model)Embedded surfacesEmbedded in E3Monge chartMinimal surfacesMinimal surfacesAsymptotic chartLorentzian manifoldsDe Sitter space dSnStatic chartAnti-de Sitter space AdSnHalf-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
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