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:

The following charts apply specifically to three-dimensional manifolds:

See also

References

  1. Sotomayor, Jorge. "On Monge's and Principal Curvature Configurations, Revised Version, Essay dedicated to the memory of Carlos T. Gutiérrez Vidalón". researchgate.net. Retrieved 1 September 2023. He settled down to work in a small desk in my room, filling out pages and more pages, which quickly exceeded the space available at the table, spreading through the floor. He performed long calculations in Monge charts and drew beautiful pictures.
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