Riemannian Gauss–Bonnet theorem
GPTKB entity
Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
even-dimensional compact orientable Riemannian manifolds
|
| gptkbp:category |
theorems in geometry
topological invariants |
| gptkbp:field |
differential geometry
|
| gptkbp:generalizes |
gptkb:classical_Gauss–Bonnet_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Riemannian Gauss–Bonnet theorem
|
| gptkbp:namedAfter |
gptkb:Carl_Friedrich_Gauss
gptkb:Pierre_Ossian_Bonnet |
| gptkbp:provenBy |
gptkb:Chern_Shiing-Shen
|
| gptkbp:relatedTo |
gptkb:Euler_characteristic
gptkb:Riemannian_manifold Gaussian curvature |
| gptkbp:state |
the integral of the curvature form over a manifold equals 2π times the Euler characteristic
|
| gptkbp:uses |
differential forms
curvature tensor |
| gptkbp:yearProved |
1944
|
| gptkbp:bfsParent |
gptkb:Riemannian_geometry
|
| gptkbp:bfsLayer |
5
|