Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
2-dimensional surfaces
|
| gptkbp:category |
theorems in geometry
|
| gptkbp:field |
differential geometry
|
| gptkbp:firstPublished |
19th century
|
| gptkbp:generalizes |
gptkb:Chern-Gauss-Bonnet_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Gauss-Bonnet theorem
|
| gptkbp:namedAfter |
gptkb:Carl_Friedrich_Gauss
gptkb:Pierre_Ossian_Bonnet |
| gptkbp:relatedTo |
gptkb:Euler_characteristic
curvature |
| gptkbp:sentence |
The integral of the Gaussian curvature over a compact 2-dimensional surface is 2π times the Euler characteristic of the surface.
|
| gptkbp:type |
global theorem
|
| gptkbp:usedIn |
gptkb:topology
gptkb:Riemannian_geometry global analysis |
| gptkbp:bfsParent |
gptkb:Riemannian_manifold
gptkb:Differential_geometry |
| gptkbp:bfsLayer |
5
|