Linked from

The 15 pages that link to Coordinate chart, each with the reason it gives.

• Coordinate systemBroader topic: Charts formalize coordinates locally when one system cannot cover an entire space.

• Metric tensorRelated: Metric components are expressed in coordinates and transform between charts.

• Tangent spaceRelated: Charts provide coordinates for computing tangent vectors.

• Covariant derivativeRelated: Coordinate formulas expose the basis variation that the covariant derivative corrects.

• Riemannian manifoldRelated: Metric components can be expressed as smooth functions in each coordinate chart.

• Smooth manifoldBroader topic: Charts provide the local coordinates whose compatibility defines smoothness.

• Coordinate transformationRelated: Charts provide the local coordinate descriptions that transformations connect.

• ManifoldBroader topic: A chart supplies the local coordinates that make a manifold look flat.

• Christoffel symbolsRelated: The symbols depend on the chart used to express the connection.

• Inverse function theoremRelated: The theorem validates local coordinates whenever the coordinate map has nonsingular derivative.

• Tensor fieldRelated: Charts let tensor fields be written as component functions.

• Coordinate singularityNarrower topic: A singularity can mark where one chart stops describing an otherwise regular space.

• General covarianceRelated: Coordinate charts change descriptions without changing the underlying geometric law.

• Differentiable manifoldBroader topic: Each chart assigns local coordinates in which smoothness can be tested.

• Two-dimensional spaceRelated: Curved two-dimensional spaces need charts to describe positions locally.