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This monograph offers the only comprehensive, coherent treatment of the theory - in characteristic 2 - of the so-called flock quadrangles, i.e., those generalized quadrangles (GQ) that arise from q-clans, along with their associated ovals. Special attention is given to the determination of the complete oval stabilizers of each of the ovals associated with a flock GQ. A concise but logically complete introduction to the basic ideas is given. The theory of these flock GQ has evolved over the past two decades and has reached a level of maturation that makes it possible for the first time to give a satisfactory, unified treatment of all the known examples. The book will be a useful resource for all researchers working in the field of finite geometry, especially those interested in finite generalized quadrangles. It is of particular interest to those studying ovals in finite Desarguesian planes. .
Finite generalized quadrangles. --- Automorphisms. --- Automorphismes --- Finite generalized quadrangles --- Automorphisms --- Algebra --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Generalized quadrangles, Finite --- Quadrangles, Generalized finite --- Mathematics. --- Convex geometry. --- Discrete geometry. --- Convex and Discrete Geometry. --- Combinatorial geometry --- Math --- Science --- Group theory --- Symmetry (Mathematics) --- Finite geometries --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry .
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Kobayashi-hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups, that were extensively studied in the 1950s-70s. The common feature of the Kobayashi-hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds.
Automorfismen. --- Hyperbolische ruimten. --- Hyperbolic spaces. --- Automorphisms. --- Espaces hyperboliques --- Automorphismes --- Electronic books. -- local. --- Probabilities. --- Topology. --- Hyperbolic spaces --- Automorphisms --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Calculus --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Probability --- Statistical inference --- Mathematics. --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Polyhedra --- Set theory --- Algebras, Linear --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Differential equations, partial. --- Partial differential equations --- Group theory --- Symmetry (Mathematics) --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean
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