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Also defined as
Elliptic, Parabolic and Hyperbolic Riemann Surface
Riemann surfaces can be categorised according to their shape:
- Riemann Surface is Path-Connected
- Riemann Surface is Second Countable
- Conformal Isomorphism of Universal Cover of Riemann Surface
- Riemann Surface is Metrizable
- Riemann Surface admits Metric of Constant Curvature
- Riemann Sphere is only Elliptic Riemann Surface
- Parabolic Riemann Surface is Plane, Punctured Plane or Torus
- Results about Riemann surfaces can be found here.
Source of Name
This entry was named for Georg Friedrich Bernhard Riemann.
This invention led directly to the Riemann Mapping Theorem.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: Riemann surface