Titlebook: Complex Kleinian Groups; Angel Cano,Juan Pablo Navarrete,José Seade Book 2013 Springer Basel 2013 Kleinian groups.complex hyperbolic geome

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Complex Hyperbolic Geometry,e constant negative holomorphic curvature. This is analogous to but different from the real hyperbolic space. In the complex case, the sectional curvature is constant on complex lines, but it changes when we consider real 2-planes which are not complex lines.

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Complex Kleinian Groups,in . that illustrates the diversity of possibilities one has when defining the notion of “limit set”. In this example we see that there are several nonequivalent such notions, each having its own interest.

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Geometry and Dynamics of Automorphisms of ,,tion for the elements in PU(2, 1) ⊂ PSL(3,.). Just as in that case, and more generally for the isometries of manifolds of negative curvature, the automorphisms of . can also be classified into the three types of elliptic, parabolic and loxodromic (or hyperbolic) elements, according to their geometry

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The Limit Set in Dimension 2,uch notions, each with its own properties and characteristics, providing each a different kind of information about the geometry and dynamics of the group. The Kulkarni limit set has the property of “quasi-minimality”, which is interesting for understanding the minimal invariant sets; and the action

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Complex Schottky Groups,s that every compact Riemann surface can be obtained as the quotient of an open set in the Riemann sphere S2 which is invariant under the action of a Schottky group. On the other hand, the limit sets of Schottky groups have rich and fascinating geometry and dynamics, which has inspired much of the c

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Kleinian Groups and Twistor Theory,s a rich interplay between the conformal geometry on even-dimensional spheres and the holomorphic on their twistor spaces. Here we follow [202] and explain how the relations between the geometry of a manifold and the geometry of its twistor space, can be carried forward to dynamics. In this way we g

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