Linked from

The 30 pages that link to Riemannian geometry, each with the reason it gives.

• Euclidean geometryNarrower topic: It generalizes geometric measurement beyond the uniformly flat setting.

• Projective geometryCompared with: It measures lengths and angles through a metric, unlike projective geometry.

• Bernhard RiemannBroader topic: Riemann generalized the geometry of curved surfaces to spaces of arbitrary dimension.

• Non-Euclidean geometryNarrower topic: It provides the broad framework for many curved geometric spaces.

• Metric tensorNarrower topic: This field takes the metric tensor as its basic geometric structure.

• Élie CartanRelated: Cartan’s methods of connections, curvature, and moving frames remain foundational tools in the field.

• Spherical geometryNarrower topic: Spherical geometry is a constant-curvature example of this broader framework.

• DivergenceRelated: A metric defines divergence on curved spaces through volume and covariant differentiation.

• Riemann curvature tensorNarrower topic: The tensor is a central invariant of this geometric theory.

• Felix KleinCompared with: Metric and curvature structures are not always captured by a single global symmetry group.

• Hermann WeylRelated: Its geometric methods shaped Weyl’s work on relativity and differential geometry.

• Affine connectionRelated: Its metric determines a canonical torsion-free affine connection.

• Levi-Civita connectionNarrower topic: The Levi-Civita connection is the standard differential structure underlying this geometry.

• Symplectic geometryCompared with: A Riemannian metric measures lengths and angles, unlike a symplectic form.

• Spherical law of cosinesNarrower topic: The spherical law is a concrete metric relation on a constant-curvature surface.

• Hilbert's axiomsCompared with: It generalizes geometric structure beyond the flat Euclidean setting axiomatized by Hilbert.

• Spherical excessNarrower topic: It provides the broader framework for measuring geometry on curved surfaces.

• Tullio Levi-CivitaBroader topic: The Levi-Civita connection is uniquely determined by a Riemannian metric.

• History of geometryBroader topic: It formalizes curved geometry and supplies the language used in general relativity.

• General covarianceNarrower topic: Its geometric language enabled laws to be formulated independently of particular coordinates.

• Marcel GrossmannBroader topic: Its geometry provided a framework for describing curved spacetime mathematically.

• Mikhail GromovNarrower topic: Gromov developed powerful methods for comparing curved spaces and their global properties.

• Hopf–Rinow theoremNarrower topic: The theorem became a foundational result in this field.

• History of general relativityBroader topic: Its mathematics gave Einstein a language for representing gravity as spacetime curvature.

• Cartan–Hadamard conjectureNarrower topic: The conjecture is a global volume question within this geometric framework.

• Classical unified field theoriesNarrower topic: Its geometric language underlies many attempts to encode fields in spacetime structure.

• RelativityRelated: Its geometric tools describe the curvature used to model gravity.

• Ricci calculusNarrower topic: Ricci calculus offers component notation for calculations in this geometric setting.

• Shape of the universeNarrower topic: It provides the language for describing curved spatial slices.

• Soul theoremNarrower topic: The theorem is a central bridge between curvature estimates and global manifold topology.