Riemann surface

File:Riemann sqrt.svg

Riemann surface for the function [math]\displaystyle{ f(z)=\sqrt z }[/math].

In mathematics, a Riemann surface is a connected one-dimensional complex manifold.

Riemann Surface Media

• The Riemann surface for the multivalued complex function f(z) = log(z) in a neighborhood of the origin. The (x, y) coordinates are the coordinates of z in the complex plane; the vertical coordinate represents the imaginary part of f(z), whose real part is represented by hue.

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  The Riemann sphere and stereographic projection.

• A simple torus fading out to a wireframe structure.

• f(z) = arcsin z

• f(z) = log z

• Riemann surface sqrt.svg

  Riemann surface of Sqrt[z], projection from 4dim C x C to 3dim C x Re(C), color is argument

• Riemann surface cube root.svg

  Riemann surface of the cube root, projection from 4dim C x C to 3dim C x Re(C), color is argument

• Riemann surface 4th root.svg

  Riemann surface of the 4th root, projection from 4dim C x C to 3dim C x Re(C), color is argument