Fuchsian modelIn mathematics, a Fuchsian model is a representation of a hyperbolic Riemann surface R as a quotient of the upper half-plane H by a Fuchsian group. Every hyperbolic Riemann surface admits such a representation. The concept is named after Lazarus Fuchs. By the uniformization theorem, every Riemann surface is either elliptic, parabolic or hyperbolic. More precisely this theorem states that a Riemann surface which is not isomorphic to either the Riemann sphere (the elliptic case) or a quotient of the complex plane by a discrete subgroup (the parabolic case) must be a quotient of the hyperbolic plane by a subgroup acting properly discontinuously and freely.
Métrique de PoincaréEn mathématiques, et plus précisément en géométrie différentielle, la métrique de Poincaré, due à Henri Poincaré, est le tenseur métrique décrivant une surface de courbure négative constante. C'est la métrique naturelle utilisée pour des calculs en géométrie hyperbolique ou sur des surfaces de Riemann.
Courbe modulaireEn théorie des nombres et en géométrie algébrique une courbe modulaire désigne la surface de Riemann, ou la courbe algébrique correspondante, construite comme quotient du demi-plan de Poincaré H sous l'action de certains sous-groupes Γ d'indice fini dans le groupe modulaire. La courbe obtenue est généralement notée Y(Γ). On appelle Γ le niveau de la courbe Y(Γ). Depuis Gorō Shimura, on sait que ces courbes admettent des équations à coefficients dans un corps cyclotomique, qui dépend du niveau Γ.
Théorème d'uniformisation de RiemannEn mathématiques, le théorème d'uniformisation de Riemann est un résultat de base dans la théorie des surfaces de Riemann, c'est-à-dire des variétés complexes de dimension 1. Il assure que toute surface de Riemann simplement connexe peut être mise en correspondance biholomorphe avec l'une des trois surfaces suivantes : le plan complexe C, le disque unité de ce plan, ou la sphère de Riemann, c'est-à-dire la droite projective complexe P1(C). Théorème d'uniformisation Transformation conforme Catégorie:Surface
Groupe discretIn mathematics, a topological group G is called a discrete group if there is no limit point in it (i.e., for each element in G, there is a neighborhood which only contains that element). Equivalently, the group G is discrete if and only if its identity is isolated. A subgroup H of a topological group G is a discrete subgroup if H is discrete when endowed with the subspace topology from G. In other words there is a neighbourhood of the identity in G containing no other element of H.
Siegel modular formIn mathematics, Siegel modular forms are a major type of automorphic form. These generalize conventional elliptic modular forms which are closely related to elliptic curves. The complex manifolds constructed in the theory of Siegel modular forms are Siegel modular varieties, which are basic models for what a moduli space for abelian varieties (with some extra level structure) should be and are constructed as quotients of the Siegel upper half-space rather than the upper half-plane by discrete groups.
Géométrie complexeIn mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis.
