Linked from

The 15 pages that link to Christoffel symbols, each with the reason it gives.

• Covariant derivativeBroader topic: They correct ordinary component derivatives for the changing coordinate basis.

• Riemann curvature tensorRelated: They provide a coordinate formula for curvature, though they are not themselves tensors.

• Affine connectionBroader topic: They give the local coefficients used to calculate covariant derivatives.

• Levi-Civita connectionBroader topic: The metric determines these coefficients through the Levi-Civita formula.

• Tensor calculusBroader topic: They make covariant-derivative calculations explicit, though they are not tensor components.

• Theorema EgregiumRelated: They express the metric’s derivatives used to compute curvature intrinsically.

• Tullio Levi-CivitaBroader topic: They provide the local coefficients used in the covariant derivatives central to his framework.

• Bianchi identitiesBroader topic: Their derivative and quadratic terms yield the coordinate form of the identities.

• Einstein notationRelated: Their indexed formulas illustrate sums over coordinate directions.

• Gregorio Ricci-CurbastroRelated: They enter the formulas for covariant differentiation in Ricci-Curbastro’s framework.

• Fundamental theorem of Riemannian geometryRelated: The theorem determines these coefficients from metric components and their derivatives.

• Geodesics in general relativityRelated: They supply the connection coefficients in the coordinate form of geodesic motion.

• Mathematics of general relativityRelated: They help calculate curvature and geodesics from metric components.

• Principle of covarianceBroader topic: They appear in covariant derivatives and compensate for changing coordinates and bases.

• Ricci calculusBroader topic: They supply the component terms needed to compute covariant derivatives.