Gauss-Bonnet theorem

Gauss-Bonnet theorem

[¦gau̇s bə′nā ‚thir·əm]
(mathematics)
The theorem that the Euler characteristic of a compact Riemannian surface is 1/(2π) times the integral over the surface of the Gaussian curvature.
References in periodicals archive ?
Two new sections look at a recent development concerning the Gauss-Bonnet theorem and scalar curvature for curved noncommutative tori, and Hopf cyclic cohomology.
Along the way he covers the geometry of curves, surfaces, curvatures, constant mean curvature surfaces, geodesics, metrics, isometries, holonomy and the Gauss-Bonnet theorem, the calculations of variations and geometry, and higher dimensions, just for fun.
This is the famous Gauss-Bonnet theorem for compact surface.
Among the topics are nearby cycles and periodicy in cyclic homology, the Gauss-Bonnet theorem for the noncommutative two torus, zeta phenomenology, absolute modular forms, the transcendence of values of transcendental functions at algebraic points, and the Hopf algebraic structure of perturbative quantum gauge theories.
Topics include the Gauss map and the second fundamental form, the divergence theorem, global extrinsic geometry, rigid motions and isometrics, and the Gauss-Bonnet theorem.