hyperbolic Riemann surface

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• Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… …   Wikipedia

• Hyperbolic group — In group theory, a hyperbolic group, also known as a word hyperbolic group, Gromov hyperbolic group, negatively curved group is a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic… …   Wikipedia

• Hyperbolic space — In mathematics, hyperbolic n space, denoted H n , is the maximally symmetric, simply connected, n dimensional Riemannian manifold with constant sectional curvature −1. Hyperbolic space is the principal example of a space exhibiting hyperbolic… …   Wikipedia

• Riemann sphere — The Riemann sphere can be visualized as the complex number plane wrapped around a sphere (by some form of stereographic projection – details are given below). In mathematics, the Riemann sphere (or extended complex plane), named after the 19th… …   Wikipedia

• Hyperbolic geometry — Lines through a given point P and asymptotic to line R. A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparall …   Wikipedia

• Surface de Bolza — Représentation en perspective de l équation y2 = x5 − x dans . En mathématiques, la surface de Bolza (du nom d Oskar Bolza) est une surface de Riemann compacte de g …   Wikipédia en Français

• Riemann solver — A Riemann solver is a numerical method used to solve a Riemann problem. They are heavily used in Computational fluid dynamics and Computational Magnetohydrodynamics.Exact SolversGodunov is credited to introduce the first exact Riemann solver for… …   Wikipedia

• Hurwitz surface — In Riemann surface theory and hyperbolic geometry, a Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely :84( g − 1) automorphisms, where g is the genus of the surface. This number is maximal by virtue of… …   Wikipedia

• Bolza surface — Perspective projection of y^2=x^5 x in mathbb C^2.In mathematics, the Bolza surface is a compact Riemann surface of genus 2 with the highest possible order of the conformal automorphism group in this genus, namely 48. An affine model for the… …   Wikipedia

• Macbeath surface — In Riemann surface theory and hyperbolic geometry, the Macbeath surface, also called Macbeath s curve or the Fricke–Macbeath curve, is the genus 7 Hurwitz surface.The automorphism group of the Macbeath surface is the simple group PSL(2,8),… …   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