Linked from

The 28 pages that link to Covariant derivative, each with the reason it gives.

• Differential geometryRelated: It is the practical differentiation tool supplied by a connection.

• Einstein field equationsRelated: It defines the conservation law compatible with curved spacetime.

• Gauge theoryRelated: It couples matter fields to the gauge connection without breaking local symmetry.

• Gauge symmetryRelated: It lets local symmetry coexist with derivatives in the equations of motion.

• Riemannian geometryRelated: It makes differentiation of vector fields meaningful across a curved manifold.

• DivergenceRelated: Its trace defines divergence for vector fields on curved spaces.

• Christoffel symbolsRelated: Christoffel symbols supply the correction terms that make coordinate derivatives geometrically meaningful.

• Yang–Mills theoryRelated: It couples matter fields to Yang–Mills gauge fields while preserving local symmetry.

• Affine connectionRelated: An affine connection is the rule that supplies covariant derivatives of vector fields.

• Levi-Civita connectionRelated: The connection is the structure that defines this derivative.

• Tensor fieldRelated: It provides a way to differentiate fields while respecting their tensor character.

• Tullio Levi-CivitaRelated: It gives tensor calculus a way to differentiate fields without losing geometric meaning.

• Bianchi identitiesRelated: Its noncommuting action underlies the curvature relation in the differential identity.

• Momentum operatorRelated: Minimal coupling replaces the ordinary derivative with a gauge-covariant one.

• General covarianceRelated: It lets physical equations express derivatives in a coordinate-independent geometric form.

• Gregorio Ricci-CurbastroRelated: It extends ordinary differentiation to the curved geometries treated by tensor calculus.

• Pauli equationRelated: It packages electromagnetic minimal coupling into a gauge-covariant operator.

• Fundamental theorem of Riemannian geometryRelated: It expresses both connection conditions in differential form.

• Mathematics of general relativityRelated: It extends differentiation to fields defined on curved spacetime.

• Principle of covarianceRelated: It lets differential equations remain tensorial in curved spacetime.

• Ricci calculusRelated: It lets Ricci calculus differentiate tensors while respecting the manifold's geometric connection.