: Mathematics: normal coordinates

topology > algebraic topology > manifold > differentiable manifold > normal coordinates

geometry > topological space > manifold > differentiable manifold > normal coordinates

geometry > differential geometry > differentiable manifold > normal coordinates

topology > differential topology > differentiable manifold > normal coordinates

geometry > analytic geometry > coordinate system > normal coordinates

normal coordinates

In differential geometry, normal coordinates at a point p in a differentiable manifold equipped with a symmetric affine connection are a local coordinate system in a neighborhood of p obtained by applying the exponential map to the tangent space at p. In a normal coordinate system, the Christoffel symbols of the connection vanish at the point p, thus often simplifying local calculations. In normal coordinates associated to the Levi-Civita connection of a Riemannian manifold, one can additionally arrange that the metric tensor is the Kronecker delta at the point p, and that the first partial derivatives of the metric at p vanish.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Normal_coordinates)

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