منابع مشابه
Riemann Surfaces
Riemann introduced his surfaces in the middle of the 19th century in order to “geometrize” complex analysis. In doing so, he paved the way for a great deal of modern mathematics such as algebraic geometry, manifold theory, and topology. So this would certainly be of interest to students in these areas, as well as in complex analysis or number theory. In simple terms, a Riemann surface is a surf...
متن کاملUniformization of Riemann Surfaces
The uniformization theorem states that every simply connected Riemann surface is conformally equivalent to the open unit disk, the complex plane, or the Riemann sphere. We present three aproaches to the uniformization of Riemann surfaces. We first prove the uniformization theorem via the construction of a harmonic function by the Dirichlet principle. We then give an alternate proof by triangula...
متن کاملAutomorphisms of Riemann Surfaces
This paper consists of mainly two parts. First it is a survey of some results on automorphisms of Riemann surfaces and Fuchsian groups. A theorem of Hurwitz states that the maximal automorphism group of a compact Riemann surface of genus 9 has order at most 84(g-1). It is well-known that the Klein quartic is the unique genus 3 curve that attains the Hurwitz bound. We will show in the second par...
متن کاملCrystallography and Riemann Surfaces
The level set of an elliptic function is a doubly periodic point set in C. To obtain a wider spectrum of point sets, we consider, more generally, a Riemann surface S immersed in C2 and its sections (“cuts”) by C. We give S a crystallographic isometry in C2 by defining a fundamental surface element as a conformal map of triangular domains and S as its extension by reflections in the triangle edg...
متن کاملNoncommutative Riemann Surfaces
We compactify M(atrix) theory on Riemann surfaces Σ with genus g > 1. Following [1], we construct a projective unitary representation of π1(Σ) realized on L (H), with H the upper half–plane. As a first step we introduce a suitably gauged sl2(R) algebra. Then a uniquely determined gauge connection provides the central extension which is a 2–cocycle of the 2nd Hochschild cohomology group. Our con...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Series A I Mathematica
سال: 1976
ISSN: 0066-1953
DOI: 10.5186/aasfm.1976.0205