Linked from

The 56 pages that link to Differential geometry, each with the reason it gives.

• Bernhard RiemannNarrower topic: Its methods provide the setting for the geometry Riemann introduced.

• TopologyCompared with: It adds smoothness and curvature to the broader topological setting.

• Algebraic geometryCompared with: It studies spaces through smooth structure rather than polynomial equations.

• Differential formNarrower topic: Differential forms are one of its central coordinate-independent languages.

• Scalar fieldNarrower topic: Scalar fields on manifolds are basic objects in differential geometry.

• Élie CartanNarrower topic: Cartan recast geometry through differential forms, moving frames, and connections.

• Arc lengthNarrower topic: Its metric ideas generalize length from plane curves to curves on spaces.

• KinematicsRelated: Its language describes trajectories and motion constrained to curved spaces.

• Analytic geometryRelated: It carries coordinate reasoning from flat figures to curved spaces.

• Felix KleinRelated: Klein’s symmetry-centered approach later informed how differential geometers describe spaces.

• GeometryBroader topic: It extends geometric analysis to curved spaces used in physics and advanced mathematics.

• ManifoldNarrower topic: Manifolds are the central spaces on which differential geometry is developed.

• Convex geometryCompared with: It emphasizes curvature and local smooth structure rather than convexity alone.

• Coordinate chartNarrower topic: Charts provide the local coordinates used to define its central constructions.

• Gauss–Bonnet theoremNarrower topic: The theorem uses differential geometry to integrate curvature across surfaces.

• CurvatureNarrower topic: Curvature is a central quantity in this framework for describing shape.

• Differential calculusRelated: It applies differential methods to geometric objects beyond ordinary functions of real variables.

• Inverse function theoremNarrower topic: Local coordinate changes on manifolds rely on the theorem's invertibility criterion.

• Algebraic curveCompared with: Its curves are often smooth paths, not necessarily solution sets of polynomial equations.

• Geometric measure theoryCompared with: It describes smooth surfaces directly, while geometric measure theory also handles nonsmooth limits.

• Lie bracketNarrower topic: Brackets of vector fields are central tools for describing smooth geometric structure.

• Tensor fieldNarrower topic: Tensor fields are among its central tools for expressing geometric structure.

• Exterior derivativeNarrower topic: The exterior derivative is a basic calculus operation on the forms used throughout the subject.

• Differential topologyCompared with: Differential geometry adds metric or connection data that differential topology does not require.

• Exterior algebraNarrower topic: Exterior algebra supplies the algebra of forms used throughout the subject.

• Tensor calculusNarrower topic: Tensor calculus supplies much of differential geometry's local computational language.

• Gaspard MongeNarrower topic: Monge’s work on curvature helped shape this broader mathematical field.

• Generalized Stokes theoremNarrower topic: The theorem’s coordinate-free formulation belongs to this broader mathematical framework.

• Ricci flowNarrower topic: Ricci flow is a central technique for studying and classifying curved spaces.

• János BolyaiRelated: Later geometry generalized the study of space beyond the constant-curvature setting of Bolyai’s work.

• Poincaré lemmaNarrower topic: The lemma is a basic local theorem in the subject.

• PseudosphereNarrower topic: The pseudosphere is a standard example connecting surface shape to intrinsic geometry.

• Theorema EgregiumNarrower topic: The theorem became a foundational result in this field.

• Tullio Levi-CivitaNarrower topic: Its geometric questions shaped Levi-Civita’s work on parallel transport and curvature.

• Erlangen programRelated: It extends the group-based perspective to spaces whose geometry varies from point to point.

• Geometric analysisNarrower topic: It supplies the manifolds, metrics, and curvature that geometric analysis investigates.

• History of geometryBroader topic: It extends the study of curvature from classical surfaces to higher-dimensional spaces.

• Gregorio Ricci-CurbastroNarrower topic: Absolute differential calculus formalized methods for studying geometry on curved spaces.

• Shiing-Shen ChernNarrower topic: Chern made this field a central setting for studying global geometric structure.

• Multivariable calculusRelated: It extends differential methods to curved spaces.

• Michael AtiyahNarrower topic: Atiyah’s work connected differential geometry with topology and analysis.

• Hilbert's theoremNarrower topic: Hilbert's theorem is a global result in the geometry of smooth surfaces.

• Solid geometryCompared with: It handles curved spaces and surfaces beyond classical measurements of solids.

• Ado's theoremNarrower topic: Matrix representations help express infinitesimal symmetries used in geometry.

• Curved spacetimeNarrower topic: It provides the language used to describe spacetime geometry.

• Jim SimonsNarrower topic: Simons first became known for research in this field before turning to finance.

• Karen UhlenbeckNarrower topic: Her contributions advanced the analysis of geometric structures on smooth manifolds.

• Clairaut's relationNarrower topic: Clairaut's relation is a classical result in the geometry of curves on surfaces.

• Classical unified field theoriesNarrower topic: Unified field research developed geometric methods that became lasting mathematical tools.

• Fáry–Milnor theoremNarrower topic: The theorem applies differential-geometric quantities to embedded curves.