parabolic Riemann surface

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• Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… …   Wikipedia

• Möbius transformation — Not to be confused with Möbius transform or Möbius function. In geometry, a Möbius transformation of the plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − …   Wikipedia

• analysis — /euh nal euh sis/, n., pl. analyses / seez /. 1. the separating of any material or abstract entity into its constituent elements (opposed to synthesis). 2. this process as a method of studying the nature of something or of determining its… …   Universalium

• mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

• Cusp neighborhood — In mathematics, a cusp neighborhood is defined as a set of points near a cusp. Cusp neighborhood for a Riemann surface The cusp neighborhood for a hyperbolic Riemann surface can be defined in terms of its Fuchsian model. Suppose that the Fuchsian …   Wikipedia

• Teichmüller space — In mathematics, given a Riemann surface X , the Teichmüller space of X , notated TX or Teich( X ), is a complex manifold whose points represent all complex structures of Riemann surfaces whose underlying topological structure is the same as that… …   Wikipedia

• List of algebraic geometry topics — This is a list of algebraic geometry topics, by Wikipedia page. Contents 1 Classical topics in projective geometry 2 Algebraic curves 3 Algebraic surfaces 4 …   Wikipedia

• Prime geodesic — In mathematics, a prime geodesic on a hyperbolic surface is a primitive closed geodesic, i.e. a geodesic which is a closed curve that traces out its image exactly once. Such geodesics are called prime geodesics because, among other things, they… …   Wikipedia

• Fuchsian model — In mathematics, a Fuchsian model is a representation of a hyperbolic Riemann surface R . By the uniformization theorem, every Riemann surface is either elliptic, parabolic or hyperbolic. Every hyperbolic Riemann surface has a non trivial… …   Wikipedia

• Modular form — In mathematics, a modular form is a (complex) analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main… …   Wikipedia

• Fuchsian group — In mathematics, a Fuchsian group is a particular type of group of isometries of the hyperbolic plane. A Fuchsian group is always a discrete group contained in the semisimple Lie group PSL(2,C). The name is given in honour of Immanuel Lazarus… …   Wikipedia