Functions of a complex variable Basic notions Concept
Riemann sphere
Summary
The Riemann sphere is the complex plane with one added point , see the definition. Stereographic projection identifies it with the unit sphere in . It is the natural domain and target of Möbius transformations and of meromorphic functions.
Where this leads
19 pages build on this one.
- Complex projective plane
- Möbius plane
- Inversive geometry
- Poincaré group
- Sullivan's no wandering domains theorem
- Wigner's classification
- Classification of Fatou components
- Complex dynamics
- Inversion in a circle
- SL(2,C)
- Kleinian group
- Lorentz group
- Representation theory of the Lorentz group
- Fatou set
- Harmonic functions on Riemann surfaces
- Julia set
- Ordinary point and singular point
- Schottky group
- Fuchsian equation
Further reading
- Web https://en.wikipedia.org/wiki/Riemann_sphere, lead section
About this page
| Tag | 0J78KBPFZB |
|---|---|
| URI | m2://0J78KBPFZB |
| Aliases | extended-complex-plane, extended-complex-numbers |
| Kind | concept |
| Writing | W1 stated |
| MSC | 30F10 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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