KnowraChern–Gauss–Bonnet theoremLinked fromLinked fromThe 4 pages that link to Chern–Gauss–Bonnet theorem, each with the reason it gives.All 4Broader topic 2Related 2Gauss–Bonnet theoremBroader topic: It extends the surface theorem’s curvature-topology relation to even dimensions.Shiing-Shen ChernBroader topic: Chern proved a higher-dimensional form of Gauss–Bonnet using characteristic forms.Bogomolov–Miyaoka–Yau inequalityRelated: It identifies the second Chern number of a smooth surface with its topological Euler characteristic.Hopf conjecture (Euler characteristic)Related: Its integrand is not generally positive under positive sectional curvature in higher dimensions.