Theorema Egregium

E29359

mathematical theorem result in differential geometry

Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.

Jump to: Surface forms Statements Referenced by

Observed surface forms (1)

Surface form	Occurrences
Gauss’s Theorema Egregium	1

Statements (44)

Predicate	Object
instanceOf	mathematical theorem ⓘ result in differential geometry ⓘ
alsoKnownAs	Theorema Egregium ⓘ surface form: Gauss’s Theorema Egregium Gauss’s remarkable theorem ⓘ
appliesTo	regular surfaces ⓘ smooth surfaces ⓘ
author	Carl Friedrich Gauss ⓘ
concerns	curved surfaces in three-dimensional Euclidean space ⓘ intrinsic curvature ⓘ metric properties of surfaces ⓘ two-dimensional surfaces ⓘ
context	classical differential geometry of surfaces ⓘ
dimension	two-dimensional manifolds ⓘ
field	Riemannian geometry ⓘ differential geometry ⓘ
historicalSignificance	first clear demonstration of intrinsic curvature of surfaces ⓘ
implies	Gaussian curvature can be computed from the first fundamental form alone ⓘ local isometry preserves Gaussian curvature ⓘ
influenced	concept of intrinsic curvature in general relativity ⓘ development of Riemannian geometry ⓘ
mainConcept	Gaussian curvature ⓘ first fundamental form ⓘ intrinsic geometry ⓘ second fundamental form ⓘ
mathematicalSubjectClassification	53A05 ⓘ
namedAfter	Latin phrase meaning remarkable theorem ⓘ
originalLanguage	Latin ⓘ
proves	Gaussian curvature ⓘ surface form: Gaussian curvature is invariant under local isometries of surfaces
publicationYear	1828 ⓘ
publishedIn	Disquisitiones Generales Circa Superficies Curvas ⓘ
relatedTo	Gauss map ⓘ Gauss–Bonnet theorem (early form) ⓘ surface form: Gauss–Bonnet theorem first fundamental form ⓘ second fundamental form ⓘ
shows	curvature of a surface can be determined by measurements within the surface ⓘ extrinsic curvature is not needed to determine Gaussian curvature ⓘ
statedBy	Carl Friedrich Gauss ⓘ
statesThat	Gaussian curvature is independent of the embedding of the surface in Euclidean space ⓘ Gaussian curvature of a surface is an intrinsic invariant ⓘ
typeOfInvariance	intrinsic invariance ⓘ
usesConcept	Christoffel symbols ⓘ coefficients of the first fundamental form ⓘ metric tensor on a surface ⓘ
yearProved	1827 ⓘ

Referenced by (4)

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

Theorema Egregium → alsoKnownAs → Theorema Egregium ⓘ

this entity surface form: Gauss’s Theorema Egregium

Carl Friedrich Gauss → notableWork → Theorema Egregium ⓘ

Gaussian curvature → relatedTo → Theorema Egregium ⓘ

Gauss–Bonnet theorem (early form) → relatedTo → Theorema Egregium ⓘ