Linked from

The 15 pages that link to Gauss–Bonnet theorem, each with the reason it gives.

• Carl Friedrich GaussRelated: It extends Gauss’s local curvature concept into a global topological result.

• Differential geometryRelated: It demonstrates how local curvature can determine a global topological invariant.

• Euler characteristicRelated: It connects this discrete invariant to geometry and curvature.

• Riemannian geometryRelated: It demonstrates a global topological consequence of integrating local curvature.

• Spherical geometryRelated: It links a spherical triangle’s angle excess to the area it encloses.

• Gaussian curvatureRelated: It turns local curvature values into a global topological constraint.

• Characteristic classRelated: It identifies an integral of curvature with the Euler class of the tangent bundle.

• Atiyah–Singer index theoremRelated: It is recovered as an index formula for the de Rham operator.

• Shiing-Shen ChernRelated: It exemplifies the link between curvature integrals and global topology that Chern extended.

• Hyperbolic triangleRelated: For a hyperbolic triangle, it equates angle deficit with curvature-weighted area.

• Hjelmslev's theoremRelated: For hyperbolic triangles, it makes angle defect proportional to area.

• Hopf conjecture (Euler characteristic)Related: In dimension two, it directly turns positive curvature into positive Euler characteristic.

• Legendre's theorem on spherical trianglesRelated: It gives a broader curvature explanation for spherical triangle angle excess.