Riemann surface

Noun

Meaning

Riemann surface (plural Riemann surfaces)

(mathematics) A one-dimensional complex manifold; a generalization of the complex plane.

Source: en.wiktionary.org

Examples

Any complex nonsingular algebraic curve viewed as a complex manifold is a Riemann surface. Source: Internet

For example, the Riemann–Roch theorem (Roch was a student of Riemann) says something about the number of linearly independent differentials (with known conditions on the zeros and poles) of a Riemann surface. Source: Internet

For the Riemann surface has parameters (the "moduli"). Source: Internet

Given a Riemann surface M, the set of all meromorphic functions defined on M is a field, denoted by C(M). Source: Internet

Note that the uniformization theorem implies that every compact Riemann surface of genus one can be represented as a torus. Source: Internet

Close letter words and terms

Riemann space Riemann sphere Riemann sum Riemann zeta function Riemann's inequality Riemann-Lebesgue lemma