In the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature...

mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that the Euler–Poincaré...

topological data). It includes many other theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications...

to the differential geometry of surfaces, including the Gauss–Bonnet theorem. Pierre Bonnet attended the Collège in Montpellier. In 1838 he entered the...

hyperbolic geometry Gauss–Bonnet theorem, a theorem about curvature in differential geometry for 2d surfaces Chern–Gauss–Bonnet theorem in differential geometry...

Gauss–Bonnet gravity, also referred to as Einstein–Gauss–Bonnet gravity, is a modification of the Einstein–Hilbert action to include the Gauss–Bonnet...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

aspects such as the Gauss–Bonnet theorem, the uniformization theorem, the von Mangoldt-Hadamard theorem, and the embeddability theorem. There are other important...

_{T}K\,dA.} A more general result is the Gauss–Bonnet theorem. Gauss's Theorema egregium (Latin: "remarkable theorem") states that Gaussian curvature of a...

geodesics. In particular, Gauss proves the local Gauss–Bonnet theorem on geodesic triangles, and generalizes Legendre's theorem on spherical triangles to...

billionaire hedge fund manager. Chern's work, most notably the Chern-Gauss-Bonnet Theorem, Chern–Simons theory, and Chern classes, are still highly influential...

the Gauss–Bonnet theorem for the two-dimensional case and the generalized Gauss–Bonnet theorem for the general case. A discrete analog of the Gauss–Bonnet...

du\,dv=\iint _{S}K\ dA} The Gauss–Bonnet theorem links total curvature of a surface to its topological properties. The Gauss map reflects many properties...

Osculating circle Curve Fenchel's theorem Theorema egregium Gauss–Bonnet theorem First fundamental form Second fundamental form Gauss–Codazzi–Mainardi equations...

This theorem has a generalization to any compact even-dimensional Riemannian manifold, see generalized Gauss-Bonnet theorem. Nash embedding theorems. They...

theorem of curves Gauss–Bonnet theorem for an elementary application of curvature Gauss map for more geometric properties of Gauss curvature Gauss's principle...

\mathbb {R} ^{3}} given as: The Gauss–Bonnet theorem relates the topology of a surface and its geometry. The Gauss–Bonnet theorem —  For each bounded surface...

curvature of the polyhedral surface concentrated at that point, and the Gauss–Bonnet theorem gives the total curvature as 2 π {\displaystyle 2\pi } times the...

0^{+}}12{\frac {\pi r^{2}-A(r)}{\pi r^{4}}}.} The theorem is closely related to the Gauss–Bonnet theorem. Berger, Marcel (2004), A Panoramic View of Riemannian...

highly abstract theorems from geometry to be used to gain insight, ranging from the Chern–Gauss–Bonnet theorem and the Riemann–Roch theorem to the Atiyah–Singer...

preserved by general diffeomorphisms of the surface. However, the famous Gauss–Bonnet theorem for closed surfaces states that the integral of the Gaussian curvature...

the Gauss–Bonnet theorem then provides a logical contradiction to the negativity of mass. As such, they were able to prove the positive mass theorem in...

topology. The digital forms of the Euler characteristic theorem and the Gauss–Bonnet theorem were obtained by Li Chen and Yongwu Rong. A 2D grid cell...

Gamas's Theorem (multilinear algebra) Gauss's Theorema Egregium (differential geometry) Gauss–Bonnet theorem (differential geometry) Gauss–Lucas theorem (complex...

uniformly, most visibly in local to global theorems in Riemannian geometry, and results like the Gauss–Bonnet theorem and Chern–Weil theory. Sharp distinctions...

Euler characteristic. The classification is consistent with the Gauss–Bonnet theorem, which implies that for a closed surface with constant curvature...

determined up to a rigid motion of R3. Bonnet's theorem is a corollary of the Frobenius theorem, upon viewing the Gauss–Codazzi equations as a system of first-order...

curvature has a clear relation to the topology of M, expressed by the Gauss–Bonnet theorem: the total scalar curvature of M is equal to 4π times the Euler characteristic...

genus is at least 1 {\displaystyle 1} . The Uniformization theorem and the Gauss–Bonnet theorem can both be applied to orientable Riemann surfaces with boundary...

Myers's theorem, also known as the Bonnet–Myers theorem, is a celebrated, fundamental theorem in the mathematical field of Riemannian geometry. It was...