In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the...

different. For example, they can look like a sphere or a torus or several sheets glued together. Examples of Riemann surfaces include graphs of multivalued...

the bijective conformal maps from the Riemann sphere to itself, i.e., the automorphisms of the Riemann sphere as a complex manifold; alternatively, they...

a point at infinity is called the Riemann sphere. If f is a function that is meromorphic on the whole Riemann sphere, then it has a finite number of zeros...

\mathbf {P} ^{1}.} This is the Bloch sphere, which can be mapped to the Riemann sphere. The Bloch sphere is a unit 2-sphere, with antipodal points corresponding...

complex numbers instead, the corresponding projective "line" is a sphere (the Riemann sphere), and then the extra point gives a 3-dimensional version of a...

the Earth can be understood mathematically as a Riemann sphere, that is, as a projection of the sphere to the complex plane. In this case, loxodromes can...

a meromorphic function can be defined for every Riemann surface. When D is the entire Riemann sphere, the field of meromorphic functions is simply the...

transformed into a perfect circle by some conformal map. A map of the Riemann sphere onto itself is conformal if and only if it is a Möbius transformation...

connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. The theorem...