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...

with Chern include Jim Simons, an American mathematician and billionaire hedge fund manager. Chern's work, most notably the Chern-Gauss-Bonnet Theorem, Chern–Simons...

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

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

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...

transversal open coverings. Notoriously, the intrinsic Chern–Gauss–Bonnet theorem proved by Chern that the Euler characteristic of a closed affine manifold...

Hsiang–Lawson's conjecture Theorema Egregium Gauss–Bonnet theorem Chern–Gauss–Bonnet theorem Chern–Weil homomorphism Gauss map Second fundamental form Curvature...

comparison theorem (Riemannian geometry) Chern–Gauss–Bonnet theorem (differential geometry) Classification of symmetric spaces (Lie theory) Darboux's theorem (symplectic...

curvature also carries over to orbifolds, along with the Chern-Gauss-Bonnet theorem and Shiing-Shen Chern's proof thereof. Satake, I. (1956), "On a generalization...

The Chern classes offer some information about this through, for instance, the Riemann–Roch theorem and the Atiyah–Singer index theorem. Chern classes...

Minister of Health Chern Shiing-Shen (陳省身; 1911–2004), Chinese-American mathematician, known for Chern–Gauss–Bonnet theorem, Chern class, Chern–Simons theory...

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

statement also follows from the Chern–Gauss–Bonnet theorem as noticed by John Milnor in 1955 (written down by Shiing-Shen Chern in 1955.). For manifolds of...

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

in the late 1940s by Shiing-Shen Chern and André Weil, in the wake of proofs of the generalized Gauss–Bonnet theorem. This theory was an important step...

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...

invariants was a particular reason to make a theory, to prove a general Gauss–Bonnet theorem. When the theory was put on an organised basis around 1950 (with...

establishing the fundamental theorems of Fourier analysis reduces to the Gaussian integral. The constant π appears in the Gauss–Bonnet formula which relates...

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

projective geometry J. A. Todd (1908–1994) Daniel Pedoe (1910–1998) Shiing-Shen Chern (1911–2004) – differential geometry Ernst Witt (1911–1991) Rafael Artzy...

differential geometry and before Chern had made history with his contributions to the generalized Gauss–Bonnet theorem and the Chern classes.) We had much to...

polyhedra. Journal of Differential Geometry 1 (1967), 245–256. (Theorem of Gauß-Bonnet for Polyhedra) Benjamin Peirce Instructor, Harvard, 1964 - 1966...

curvature has a clear relation to the topology of M, expressed by the Gauss–Bonnet theorem: the total scalar curvature of M(being equal to twice the Gaussian...

circle is 0. Vandermonde polynomial Thom isomorphism Generalized Gauss–Bonnet theorem Chern class Pontryagin class Stiefel-Whitney class Bott, Raoul and Tu...

the metrics appearing from the uniformization theorem. More generally, according to the Chern-Gauss-Bonnet formula, if M is a closed and connected manifold...

Foucault pendulum, the path is a circle of latitude, and by the Gauss–Bonnet theorem, the phase shift is given by the enclosed solid angle. In a near-inertial...

formula might be understood as an infinite-dimensional analogue of the Gauss–Bonnet theorem. At a later date, this theory was further developed and became the...

elementary but novel combination of the Gauss equation, the formula for second variation of area, and the Gauss-Bonnet theorem, Schoen and Yau were able to rule...

} The Euler characteristic; this follows from the work of Chern on the Gauss-Bonnet theorem, where such μ {\displaystyle \mu } and ω {\displaystyle \omega...