Riemann surface oor Fins
Riemann surface
en
(mathematics) a one-dimensional complex manifold; a generalization of the complex plane
Vertalings in die woordeboek Engels - Fins
pinta
en
manifold
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Ahlfors wrote several other significant books, including Riemann surfaces (1960) and Conformal invariants (1973).
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The complex plane C is the most basic Riemann surface.
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More generally, every non-empty open subset of a Riemann surface is a Riemann surface.
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As a complex manifold of 1 complex dimension (i.e., 2 real dimensions), this is also called a Riemann surface.
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Note that the uniformization theorem implies that every compact Riemann surface of genus one can be represented as a torus.
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It is also an isomorphism of Riemann surfaces from the torus to the cubic curve, so topologically, an elliptic curve is a torus.
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During 1879, he examined the action of PSL(2,7), considered as an image of the modular group, and obtained an explicit representation of a Riemann surface now termed the Klein quartic.
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Among Rolf Nevanlinna's later interests in mathematics were the theory of Riemann surfaces (the monograph Uniformisierung in 1953) and functional analysis (Absolute analysis in 1959, written in collaboration with his brother Frithiof).
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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.
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It is also an isomorphism of Riemann surfaces, so topologically, a given elliptic curve looks like a torus.
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More generally, every open subset of a Riemann surface is a Riemann surface.
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4 On Riemann surfaces
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These results and the Uniformization Theorem of simply-connected Riemann surfaces will be used to prove a Uniformization Theorem for general Riemann surfaces.
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The realm of Riemann surfaces can be divided into three regimes: hyperbolic, parabolic and elliptic Riemann surfaces, with the distinction given by the uniformization theorem.
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Ahlfors (18 April 1907 – 11 October 1996) was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his text on complex analysis.
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