In the mathematical field of
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Gauss–Bonnet theorem — The Gauss–Bonnet theorem or Gauss–Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic). It is named … Wikipedia
Generalized Gauss–Bonnet theorem — In mathematics, the generalized Gauss–Bonnet theorem (also called Chern–Gauss–Bonnet theorem) presents the Euler characteristic of a closed even dimensional Riemannian manifold as an integral of a certain polynomial derived from its curvature. It … Wikipedia
Generalized Gauss-Bonnet theorem — In mathematics, the generalized Gauss Bonnet theorem presents the Euler characteristic of a closed even dimensional Riemannian manifold as an integral of a certain polynomial derived from its curvature. It is a direct generalization of the Gauss… … Wikipedia
Bonnet's theorem — 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) albeit with different speeds v 1, v 2,..., v n at a given point P , then the same orbit… … Wikipedia
Pierre Ossian Bonnet — (22 December 1819, Montpellier – 22 June 1892, Paris) was a French mathematician. He made some important contributions to the differential geometry of surfaces, including the Gauss Bonnet theorem. Con … Wikipedia
Nash embedding theorem — The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space. Isometric means preserving the length of every path. For instance,… … Wikipedia
Hurwitz's automorphisms theorem — In mathematics, Hurwitz s automorphisms theorem bounds the group of automorphisms, via orientation preserving conformal mappings, of a compact Riemann surface of genus g > 1, telling us that the order of the group of such automorphisms is bounded … Wikipedia
Bertrand–Diquet–Puiseux theorem — In the mathematical study of the differential geometry of surfaces, the Bertrand–Diquet–Puiseux theorem expresses the Gaussian curvature of a surface in terms of the circumference of a geodesic circle, or the area of a geodesic disc. The theorem… … Wikipedia
Uniformization theorem — In mathematics, the uniformization theorem for surfaces says that any surface admits a Riemannian metric of constant Gaussian curvature. In fact, one can find a metric with constant Gaussian curvature in any given conformal class.In other words… … Wikipedia
Myers's theorem — The Myers theorem, also known as the Bonnet–Myers theorem, is a classical theorem in Riemannian geometry. The strong form was proven by Sumner Byron Myers. The theorem states that if Ricci curvature of a complete Riemannian manifold M is bounded… … Wikipedia
