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Riemann surface

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In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together.

Riemann surface - Wikipedia Jump to content From Wikipedia, the free encyclopedia One-dimensional complex manifold Not to be confused with Riemannian surface or Riemannian manifold . For the Riemann surface of a subring of a field, see Zariski–Riemann space . The Riemann surface for the multivalued complex function f ( z ) = log ⁡ ( z ) {\displaystyle f(z)=\log(z)} in a neighborhood of the origin. The ( x , y ) {\displaystyle (x,y)} coordinates are the coordinates of z {\displaystyle z} in the complex plane; the vertical coordinate represents the imaginary part of f ( z ) {\displaystyle f(z)}

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