For a compact oriented Riemannian 2-manifold M without boundary, ∫_M K dA = 2π χ(M). Connects local curvature to global topology; generalises to Chern–Gauss–Bonnet in higher dimensions.
For a compact oriented Riemannian 2-manifold M without boundary, ∫_M K dA = 2π χ(M). Connects local curvature to global topology; generalises to Chern–Gauss–Bonnet in higher dimensions.