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Geometry --- Geometry, Hyperbolic. --- Géométrie hyperbolique --- Géométrie hyperbolique
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Geometry, Hyperbolic --- Hyperbolic spaces --- Géométrie hyperbolique --- Espaces hyperboliques --- Géométrie hyperbolique
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Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point of view; first the density is defined and then the metric via integration. The study of hyperbolic geometry in arbitrary domains requires the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. These ideas are developed in the context of what is used later. The authors then provide a detailed discussion of hyperbolic geometry for arbitrary plane domains. New material on hyperbolic and hyperbolic-like metrics is presented. These are generalizations of the Kobayashi and Caratheodory metrics for plane domains. The book concludes with applications to holomorphic dynamics including new results and accessible open problems.
Geometry, Hyperbolic --- Géométrie hyperbolique --- Geometry, Hyperbolic. --- Geometry, Non-Euclidean. --- Non-Euclidean geometry --- Geometry --- Parallels (Geometry) --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Geometry, Non-Euclidean --- Foundations
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Convex geometry. --- Geometry, Hyperbolic. --- Differentiable dynamical systems. --- Functions of several complex variables. --- Convex bodies. --- Random walks (Mathematics) --- Géométrie convexe --- Géométrie hyperbolique --- Dynamique différentiable --- Fonctions de plusieurs variables complexes --- Corps convexes --- Promenades aléatoires (Mathématiques)
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Geometry --- 514.14 --- -Geometry, Projective --- Projective geometry --- Geometry, Modern --- Mathematics --- Euclid's Elements --- Affine geometry. Projective geometry --- Foundations --- Geometry, Projective. --- Geometry. --- Foundations. --- 514.14 Affine geometry. Projective geometry --- Geometry, Projective --- Foundations of geometry --- Geometry, Non-Euclidean --- Parallels (Geometry) --- Philosophy --- Geometry, projective --- Géométrie euclidienne --- Géométrie analytique --- Geometry, Analytic --- Géométrie hyperbolique --- Geometry, Hyperbolic --- Géométrie de Riemann --- Geometry, Riemannian --- Geometry - Foundations --- Géométrie euclidienne --- Géométrie analytique --- Géométrie hyperbolique --- Géométrie de Riemann
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Discrete groups --- Isometrics (Mathematics) --- Möbius transformations --- Geometry, Hyperbolic --- Groupes discrets --- Isométrie (Mathématiques) --- Möbius, Transformations de --- Géométrie hyperbolique --- 514.16 --- Mobius transformations --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Geometry, Non-Euclidean --- Transformations (Mathematics) --- Groups, Discrete --- Infinite groups --- Geometries over algebras --- 514.16 Geometries over algebras --- Möbius transformations --- Isométrie (Mathématiques) --- Möbius, Transformations de --- Géométrie hyperbolique --- Discrete groups. --- Discrete mathematics
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514.13 --- Geometry, Non-Euclidean --- Non-Euclidean geometry --- Geometry --- Parallels (Geometry) --- Non-Euclidean metric geometries. Lobachevsky geometry. Other hyperbolic geometries. Elliptic geometries --- Foundations --- Geometry, Non-Euclidean. --- 514.13 Non-Euclidean metric geometries. Lobachevsky geometry. Other hyperbolic geometries. Elliptic geometries --- Géométrie non-euclidienne. --- Géométrie de Riemann --- Geometry, Riemannian --- Géométrie hyperbolique --- Geometry, Hyperbolic --- Géométrie non-euclidienne. --- Géométrie de Riemann --- Géométrie hyperbolique
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This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty.
Topology --- Differential geometry. Global analysis --- Geometry, Hyperbolic --- Three-manifolds (Topology) --- Géométrie hyperbolique --- Variétés topologiques à 3 dimensions --- Geometry, Hyperbolic. --- 514.1 --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Geometry, Non-Euclidean --- General geometry --- Three-manifolds (Topology). --- 514.1 General geometry --- Géométrie hyperbolique --- Variétés topologiques à 3 dimensions --- 3-sphere. --- Abelian group. --- Affine space. --- Affine transformation. --- Atlas (topology). --- Automorphism. --- Basis (linear algebra). --- Bounded set (topological vector space). --- Brouwer fixed-point theorem. --- Cartesian coordinate system. --- Characterization (mathematics). --- Compactification (mathematics). --- Conformal map. --- Contact geometry. --- Curvature. --- Cut locus (Riemannian manifold). --- Diagram (category theory). --- Diffeomorphism. --- Differentiable manifold. --- Dimension (vector space). --- Dimension. --- Disk (mathematics). --- Divisor (algebraic geometry). --- Dodecahedron. --- Eigenvalues and eigenvectors. --- Embedding. --- Euclidean space. --- Euler number. --- Exterior (topology). --- Facet (geometry). --- Fiber bundle. --- Foliation. --- Fundamental group. --- Gaussian curvature. --- Geometry. --- Group homomorphism. --- Half-space (geometry). --- Holonomy. --- Homeomorphism. --- Homotopy. --- Horocycle. --- Hyperbolic geometry. --- Hyperbolic manifold. --- Hyperbolic space. --- Hyperboloid model. --- Interior (topology). --- Intersection (set theory). --- Isometry group. --- Isometry. --- Jordan curve theorem. --- Lefschetz fixed-point theorem. --- Lie algebra. --- Lie group. --- Line (geometry). --- Linear map. --- Linearization. --- Manifold. --- Mathematical induction. --- Metric space. --- Moduli space. --- Möbius transformation. --- Norm (mathematics). --- Pair of pants (mathematics). --- Piecewise linear manifold. --- Piecewise linear. --- Poincaré disk model. --- Polyhedron. --- Projection (linear algebra). --- Projection (mathematics). --- Pseudogroup. --- Pullback (category theory). --- Quasi-isometry. --- Quotient space (topology). --- Riemann mapping theorem. --- Riemann surface. --- Riemannian manifold. --- Sheaf (mathematics). --- Sign (mathematics). --- Simplicial complex. --- Simply connected space. --- Special linear group. --- Stokes' theorem. --- Subgroup. --- Subset. --- Tangent space. --- Tangent vector. --- Tetrahedron. --- Theorem. --- Three-dimensional space (mathematics). --- Topological group. --- Topological manifold. --- Topological space. --- Topology. --- Transversal (geometry). --- Two-dimensional space. --- Uniformization theorem. --- Unit sphere. --- Variable (mathematics). --- Vector bundle. --- Vector field. --- Topologie algébrique --- Topologie combinatoire --- Algebraic topology. --- Combinatorial topology. --- Variétés topologiques --- Geometrie --- Theorie des noeuds
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