Examples of 'riemann sphere' in a sentence
Meaning of "riemann sphere"
riemann sphere - a concept in mathematics and complex analysis that extends the complex numbers to include a point at infinity. The Riemann sphere is used to represent the complex plane with an added point at infinity, providing a geometric interpretation for mapping functions and understanding complex functions
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- The complex numbers extended with the number ∞; the complex plane (representation of the complex numbers as a Euclidean plane) extended with a single idealised point at infinity and consequently homeomorphic to a sphere in 3-dimensional Euclidean space.
- The 2-sphere embedded in Euclidean three-dimensional space and often represented as a unit sphere, regarded as a homeomorphic representation of the extended complex plane and thus the extended complex numbers.
How to use "riemann sphere" in a sentence
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riemann sphere
Global conformal maps on the Riemann sphere.
The Riemann sphere has many uses in physics.
Thus the unit sphere is diffeomorphic to the Riemann sphere.
The Riemann sphere is one example.
The complex projective line is also called the Riemann sphere.
The Riemann sphere.
Suppose that z is a holomorphic local coordinate for the Riemann sphere.
The sphere is called the Riemann Sphere in honor of Bernhard Riemann.
The complex plane extended by a point at infinity is called the Riemann sphere.
However, the Riemann sphere is not merely a topological sphere.
A common instance is the complex plane where the compactification corresponds to the Riemann sphere.
In complex analysis, the Riemann sphere facilitates an elegant theory of meromorphic functions.
So its image Ω is open in the Riemann sphere.
Topologically, the Riemann sphere is the one-point compactification of the complex plane.
With respect to this group, the sphere is equivalent to the usual Riemann sphere.
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For example, the automorphisms of the Riemann sphere are Möbius transformations.
In practice the point 0 is often transformed into the point ∞ of the Riemann sphere.
The Riemann sphere is only a conformal manifold, not a Riemannian manifold.
Using these definitions, f becomes a continuous function from the Riemann sphere to itself.
The projective linear group PGL ( 2,C ) acts on the Riemann sphere by the Möbius transformations.
Since the transition maps are holomorphic, they define a complex manifold, called the Riemann sphere.
Complex structure ; see Riemann sphere.
However, there always exist non-constant meromorphic functions holomorphic functions with values in the Riemann sphere C ∪ { ∞.
For example, consider a CFT on the Riemann sphere.
This turns H * into a topological space which is a subset of the Riemann sphere P1C.
In addition, the two-sphere is equivalent to the Riemann sphere.
Specifically, it 's called the Riemann Sphere.
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Another important sphere is that of combined transport
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You could make a sphere in this studio
Examples of using Riemann
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Riemann made major contributions to real analysis
Contraction of riemann tensor
Riemann surfaces and the theta function
