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...

In classical mechanics, Bonnet's theorem states that if n different force fields each produce the same geometric orbit (say, an ellipse of given dimensions)...

uniquely 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...

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

dA.} A more general result is the Gauss–Bonnet theorem. Gauss's Theorema egregium (Latin: "remarkable theorem") states that Gaussian curvature of a surface...

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

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

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 theorem...

{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 M {\displaystyle...

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

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

Gauss–Bonnet theorem Hopf–Rinow theorem Cartan–Hadamard theorem Myers theorem Rauch comparison theorem Morse index theorem Synge theorem Weinstein theorem Toponogov...

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...

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

theorem (proof theory) Deduction theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem...

Gauss–Bodenmiller theorem – described on website of University of Crete Gauss–Bolyai–Lobachevsky space, a hyperbolic geometry Gauss–Bonnet theorem, a theorem about...

resembles a local maximum or minimum (positive curvature). The Gauss–Bonnet theorem gives the total curvature as 2 π {\displaystyle 2\pi } times the Euler...

polyhedra, is the (angular) defect; the analog for the Gauss–Bonnet theorem is Descartes' theorem on total angular defect. Because (Gaussian) curvature can...

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...

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...

a topological surface term. This follows from the generalized Gauss–Bonnet theorem on a 4D manifold 1 8 π 2 ∫ d 4 x − g G = χ ( M ) {\displaystyle {\frac...

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 the...

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

{\displaystyle (-1)^{d}} . For surfaces, these statements follow from the Gauss–Bonnet theorem. For four-dimensional manifolds, this follows from the finiteness of...

Alexandrov's theorem on polyhedra is a rigidity theorem in mathematics, describing three-dimensional convex polyhedra in terms of the distances between...

triangle's angular defect is understood as a special case of the Gauss-Bonnet theorem where the curvature of a closed curve is not a function, but a measure...

The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: A physical...

ellipses, as a solution of the Kepler problem. Therefore, according to Bonnet's theorem, the same ellipses are the solutions for the Euler problem. Introducing...

differential-geometric proofs which relate it to the Gauss–Bonnet theorem. The Second Fundamental Theorem can also be derived from the metric-topological theory...