Linked from

The 24 pages that link to Riemann curvature tensor, each with the reason it gives.

• General relativityBroader topic: Its contractions provide the curvature terms used in Einstein’s field equations.

• Differential geometryBroader topic: It captures how a connection departs from flat Euclidean behavior.

• Bernhard RiemannBroader topic: It gives a precise local measure of the curvature implicit in Riemann’s geometric framework.

• Einstein field equationsBroader topic: The equations use contractions of curvature to express how spacetime bends.

• Riemannian geometryBroader topic: It encodes the manifold's full intrinsic curvature.

• Covariant derivativeRelated: Commuting this derivative in different directions produces the curvature tensor.

• Riemannian manifoldRelated: It records how the manifold’s geometry departs locally from flat Euclidean geometry.

• Riemannian metricRelated: The metric's variation determines the manifold's intrinsic curvature.

• TensorBroader topic: It is a prominent example of a tensor field built from geometric structure.

• Christoffel symbolsRelated: Its coordinate formula combines derivatives and products of Christoffel symbols.

• Ricci curvatureNarrower topic: Ricci curvature is its trace over two tensor indices.

• Levi-Civita connectionRelated: Applying the connection twice reveals the manifold's intrinsic curvature.

• Tensor calculusBroader topic: It records the curvature revealed by repeated covariant differentiation.

• Ricci flowNarrower topic: Ricci curvature is obtained by contracting this fuller description of curvature.

• Coordinate singularityRelated: Its geometric content does not depend on a particular coordinate chart.

• Theorema EgregiumNarrower topic: The theorem is the surface case of the broader link between metric and intrinsic curvature.

• Tullio Levi-CivitaRelated: Levi-Civita’s methods made curvature computations systematic in tensor notation.

• Bianchi identitiesNarrower topic: The identities express differential constraints on this curvature tensor.

• Gregorio Ricci-CurbastroRelated: It is a key geometric quantity expressible through the differential methods Ricci-Curbastro developed.

• Marcel GrossmannBroader topic: It formalizes the spacetime curvature central to Einstein’s gravitational theory.

• Raychaudhuri equationNarrower topic: Its contraction appears in the equation as the Ricci-curvature focusing term.

• Curved spacetimeBroader topic: Its components describe the local curvature represented by the model.

• Fundamental theorem of Riemannian geometryRelated: The Levi-Civita connection provides the derivatives from which Riemannian curvature is formed.

• Ricci calculusBroader topic: Ricci notation provides a compact route from connection coefficients to this central curvature tensor.