Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
2-dimensional surfaces
|
| gptkbp:category |
gptkb:topology
differential geometry theorems in geometry |
| gptkbp:field |
differential geometry
|
| 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:publishedIn |
gptkb:Journal_für_die_reine_und_angewandte_Mathematik
|
| gptkbp:relatedTo |
gptkb:Euler_characteristic
curvature |
| gptkbp:state |
The integral of Gaussian curvature over a compact 2-dimensional surface plus the integral of geodesic curvature along the boundary equals 2π times the Euler characteristic of the surface.
|
| gptkbp:yearProposed |
1848
|
| gptkbp:bfsParent |
gptkb:Atiyah–Singer_index_theorem
gptkb:Riemannian_geometry |
| gptkbp:bfsLayer |
5
|