For closed orientable surface S: int_S K dA = 2 pi chi(S) where K is Gauss curvature and chi Euler characteristic; topological invariant from local geometry; generalizes to higher dim via Chern-Gauss-Bonnet.
For closed orientable surface S: int_S K dA = 2 pi chi(S) where K is Gauss curvature and chi Euler characteristic; topological invariant from local geometry; generalizes to higher dim via Chern-Gauss-Bonnet.