Generalized Gauss-Bonnet theorem
Teorema de Gauss-Bonnet generalizado
- Date
- 1944 · confidence high
- Place
- Princeton, New Jersey, United States
- Credited to
- Shiing-Shen Chern
- Field
- Knowledge & symbols
What was discovered
A generalization to closed even-dimensional Riemannian manifolds of the classical Gauss-Bonnet theorem, relating the Euler-Poincaré characteristic (a topological invariant) to the integral of curvature (an analytical invariant); proved by Shiing-Shen Chern at the Institute for Advanced Study.
What it led to
- Foundational result in differential geometry and topology
- Basis for Chern-Weil theory
- Precursor to index theorems such as Atiyah-Singer