(of a riemann surface)
1Riemann 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… …
2riemann surface — noun Usage: usually capitalized R Etymology: after G.F.B. Riemann : a multilayered surface in the theory of complex functions on which a multivalued complex function can be treated as a single valued function of a complex variable * * * Math. a… …
3Riemann surface — Math. a geometric representation of a function of a complex variable in which a multiple valued function is depicted as a single valued function on several planes, the planes being connected at some of the points at which the function takes on… …
4Compact Riemann surface — In mathematics, a compact Riemann surface is a complex manifold of dimension one that is a compact space. Riemann surfaces are generally classified first into the compact (those that are closed manifolds) and the open (the rest, which from the… …
5Riemann surface — noun a one dimensional complex manifold; a generalization of the complex plane …
6Riemann 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… …
7Surface — This article discusses surfaces from the point of view of topology. For other uses, see Differential geometry of surfaces, algebraic surface, and Surface (disambiguation). An open surface with X , Y , and Z contours shown. In mathematics,… …
8Riemann–Roch theorem — In mathematics, specifically in complex analysis and algebraic geometry, the Riemann–Roch theorem is an important tool in the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates… …
9Riemann hypothesis — The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011 …
10Riemann, Bernhard — ▪ German mathematician in full Georg Friedrich Bernhard Riemann born September 17, 1826, Breselenz, Hanover [Germany] died July 20, 1866, Selasca, Italy German mathematician whose profound and novel approaches to the study of geometry laid the …
