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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...

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

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

density theorem (number theory) Chen's theorem (number theory) Cheng's eigenvalue comparison theorem (Riemannian geometry) Chern–Gauss–Bonnet theorem (differential...

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...

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

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...

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...

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...

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

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

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...