Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Generalized_Gauss–Bonnet_theorem> ?p ?o. }
Showing items 1 to 14 of
14
with 100 items per page.
- Generalized_Gauss–Bonnet_theorem abstract "In mathematics, the generalized Gauss–Bonnet theorem (also called Chern–Gauss–Bonnet theorem) presents the Euler characteristic of a closed even-dimensional Riemannian manifold as an integral of a certain polynomial derived from its curvature. It is a direct generalization of the Gauss–Bonnet theorem (named after Carl Friedrich Gauss and Pierre Ossian Bonnet) to higher dimensions.Let M be a compact orientable 2n-dimensional Riemannian manifold without boundary, and let be the curvature form of the Levi-Civita connection. This means that is an -valued 2-form on M. So can be regarded as a skew-symmetric 2n × 2n matrix whose entries are 2-forms, so it is a matrix over the commutative ring . One may therefore take the Pfaffian of , , which turns out to be a 2n-form.The generalized Gauss–Bonnet theorem states thatwhere denotes the Euler characteristic of M.".
- Generalized_Gauss–Bonnet_theorem wikiPageID "393115".
- Generalized_Gauss–Bonnet_theorem wikiPageRevisionID "590116428".
- Generalized_Gauss–Bonnet_theorem subject Category:Theorems_in_differential_geometry.
- Generalized_Gauss–Bonnet_theorem comment "In mathematics, the generalized Gauss–Bonnet theorem (also called Chern–Gauss–Bonnet theorem) presents the Euler characteristic of a closed even-dimensional Riemannian manifold as an integral of a certain polynomial derived from its curvature.".
- Generalized_Gauss–Bonnet_theorem label "Generalized Gauss–Bonnet theorem".
- Generalized_Gauss–Bonnet_theorem label "Teorema de Gauss-Bonnet generalizado".
- Generalized_Gauss–Bonnet_theorem label "Veralgemeende stelling van Gauss-Bonnet".
- Generalized_Gauss–Bonnet_theorem sameAs Generalized_Gauss%E2%80%93Bonnet_theorem.
- Generalized_Gauss–Bonnet_theorem sameAs Teorema_de_Gauss-Bonnet_generalizado.
- Generalized_Gauss–Bonnet_theorem sameAs Veralgemeende_stelling_van_Gauss-Bonnet.
- Generalized_Gauss–Bonnet_theorem sameAs Q11704319.
- Generalized_Gauss–Bonnet_theorem sameAs Q11704319.
- Generalized_Gauss–Bonnet_theorem wasDerivedFrom Generalized_Gauss–Bonnet_theorem?oldid=590116428.