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 diffe...
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http://en.wikipedia.org/wiki/Riemann_surface
(from the article `analysis`) ...of higher-dimensional spaces. Sometimes the geometry guided the development of concepts in analysis, and sometimes it was the reverse. A beautiful ... ...real variables + (where = 1), an equation involving two complex variables defines a real surface—now known as a Riemann sur...
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http://www.britannica.com/eb/a-z/r/48
Also known as a complex curve, a complex manifold with one complex dimension. The Riemann surface is a conformal structure.
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http://www.daviddarling.info/encyclopedia/R/Riemann_surface.html
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