differential geometry

E287407

branch of mathematics field of study mathematical discipline

Differential geometry is a branch of mathematics that uses the techniques of calculus and linear algebra to study the properties and curvature of smooth shapes and spaces such as curves, surfaces, and manifolds.

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All labels observed (2)

Label	Occurrences
differential geometry canonical	2
Riemannian geometry	1

Statements (68)

Predicate	Object
instanceOf	branch of mathematics ⓘ field of study ⓘ mathematical discipline ⓘ
appliesTo	abstract manifolds ⓘ curves in Euclidean space ⓘ surfaces in Euclidean space ⓘ
developedBy	Bernhard Riemann ⓘ Carl Friedrich Gauss ⓘ Gregorio Ricci-Curbastro ⓘ Tullio Levi-Civita ⓘ Élie Cartan ⓘ
formalizedIn	19th century ⓘ
hasSubfield	Finsler geometry ⓘ Lorentzian geometry ⓘ Riemannian manifolds ⓘ surface form: Riemannian geometry affine differential geometry ⓘ complex differential geometry ⓘ contact geometry ⓘ global differential geometry ⓘ symplectic geometry ⓘ
historicalDevelopmentFrom	classical geometry of curves and surfaces ⓘ
keyConcept	Christoffel symbols ⓘ Gaussian curvature ⓘ Jacobi fields ⓘ Levi-Civita connection ⓘ Ricci curvature ⓘ Riemann curvature tensor ⓘ exponential map ⓘ mean curvature ⓘ minimal surfaces ⓘ parallel transport ⓘ scalar curvature ⓘ sectional curvature ⓘ
mathematicsSubjectClassification	53-XX ⓘ
relatedTo	algebraic geometry ⓘ differential topology ⓘ mathematical physics ⓘ topology ⓘ
studies	Lie algebras ⓘ Lie group ⓘ surface form: Lie groups Riemannian manifolds ⓘ complex manifolds ⓘ connections ⓘ curvature ⓘ differential forms ⓘ foliations ⓘ geodesics ⓘ manifolds ⓘ metrics ⓘ principal bundles ⓘ smooth curves ⓘ smooth surfaces ⓘ submanifolds ⓘ symplectic manifolds ⓘ vector bundles ⓘ
usedIn	computer graphics ⓘ computer vision ⓘ continuum mechanics ⓘ control theory ⓘ gauge theory ⓘ general relativity ⓘ robotics ⓘ string theory ⓘ
uses	calculus ⓘ differential topology ⓘ linear algebra ⓘ multivariable calculus ⓘ tensor calculus ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Ricci scalar → fieldOfStudy → differential geometry ⓘ

rotation group SO(3) → appearsIn → differential geometry ⓘ

subject surface form: SO(3)

Optimal Transport: Old and New → subject → differential geometry ⓘ

this entity surface form: Riemannian geometry