What does riemann surface mean?
Definitions for riemann surface
rie·man·n sur·face
This dictionary definitions page includes all the possible meanings, example usage and translations of the word riemann surface.
Wiktionary
Riemann surfacenoun
A one-dimensional complex manifold; a generalization of the complex plane.
Etymology: From Bernhard Riemann German mathematician
Wikidata
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold. 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. For example, they can look like a sphere or a torus or a couple of sheets glued together. The main point of Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are nowadays considered the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm. Every Riemann surface is a two-dimensional real analytic manifold, but it contains more structure which is needed for the unambiguous definition of holomorphic functions. A two-dimensional real manifold can be turned into a Riemann surface if and only if it is orientable and metrizable. So the sphere and torus admit complex structures, but the Möbius strip, Klein bottle and projective plane do not.
Numerology
Chaldean Numerology
The numerical value of riemann surface in Chaldean Numerology is: 6
Pythagorean Numerology
The numerical value of riemann surface in Pythagorean Numerology is: 3
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"riemann surface." Definitions.net. STANDS4 LLC, 2024. Web. 1 May 2024. <https://www.definitions.net/definition/riemann+surface>.
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