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In mathematics, a Kleinian model is a model of a three-dimensional hyperbolic manifold N by the quotient space where is a discrete subgroup of PSL(2,C). Here, the subgroup , a Kleinian group, is defined so that it is isomorphic to the fundamental group of the surface N. Many authors use the terms Kleinian group and Kleinian model interchangeably, letting one stand for the other. The concept is named after Felix Klein.
Many properties of Kleinian models are in direct analogy to those of Fuchsian models; however, overall, the theory is less well developed. A number of unsolved conjectures on Kleinian models are the analogs to theorems on Fuchsian models.
In mathematics, a Kleinianmodel is a model of a three-dimensional hyperbolic manifold N by the quotient space H 3 / Γ {\displaystyle \mathbb {H} ^{3}/\Gamma...
In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space H3. The latter, identifiable...
connection, which can be handled either as a type of Cartan connection modelled on the associated Möbius geometry, or as a Weyl connection. This allows...
functions that projective identification may serve. As in the traditional Kleinianmodel, it serves as a defense. Projective identification serves as a mode...
analogous construction for three-dimensional hyperbolic surfaces is the Kleinianmodel. Dini's surface Hyperbolic 3-manifold Ideal polyhedron Mostow rigidity...
the Kleinianmodel, an analogous construction for 3-manifolds Fundamental polygon Matsuzaki, K.; Taniguchi, M.: Hyperbolic manifolds and Kleinian groups...
inequality Klein model Klein polyhedron Klein surface Klein quadric Klein quartic Kleinian group Kleinian integer KleinianmodelKleinian ring Kleinian singularity...
Hyperbolic 3-manifold Hyperbolic manifold Hyperbolic set Hyperbolic tree Kleinian group Lambert quadrilateral Open universe Poincaré metric Saccheri quadrilateral...
of the upper half-plane model of the hyperbolic plane. A Fuchsian group is sometimes considered as a special case of a Kleinian group, by embedding the...
Donald Meltzer (1922–2004) was a Kleinian psychoanalyst whose teaching made him influential in many countries. He became known for making clinical headway...
the following table, there is a description of the classical geometries, modeled as Klein geometries. R. W. Sharpe (1997). Differential Geometry: Cartan's...
(Ratcliffe 1994, 12.7). Density theorem for Kleinian groups Greenberg, L. (1966), "Fundamental polyhedra for kleinian groups", Annals of Mathematics, Second...
Psychoanalytical Society split into three separate training divisions: (1) Kleinian, (2) Freudian, and (3) Independent. These debates finally ceased[when?]...
a Kleinian group (a discrete subgroup of PSL(2,C)) which is conjugate to a subgroup of PSL(2,R). Fuchsian groups are used to create Fuchsian models of...
Bers' density conjecture from singly degenerate Kleinian surface groups to all finitely generated Kleinian groups in the late 1970s and early 1980s. The...
Kleinian surface groups. I. Models and bounds, arXiv:math/0302208, Bibcode:2003math......2208M Minsky, Yair (2010), "The classification of Kleinian surface...
discussions" (1942–44) at the British Psychoanalytical Association. The Kleinian psychologists proposed that "underlying the Oedipus complex, as Freud described...
surface singularity, Kleinian singularity, or rational double point, is an isolated singularity of a complex surface which is modeled on a double branched...
by Robert W. Brooks and Peter Matelski in 1978, as part of a study of Kleinian groups. Afterwards, in 1980, Benoit Mandelbrot obtained high-quality visualizations...
5, 401–487. Thurston, William P. (1982). "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry". Bulletin of the American Mathematical...
NJ: Erlbaum. O'Connor, John (1 December 2002). "Type A, type b and the kleinian positions: do they relate to similar processes?". Psychoanalytic Psychology...
theory. The research facility Klein established at Göttingen served as model for the best such facilities throughout the world. He introduced weekly...
tool in the study of Kleinian groups. For example, it has been used in the proof of the ending lamination conjecture. A possible model for random 3-manifolds...
amicable groups within the psychoanalytic movement: the "Freudians", the "Kleinians", and the "Middle Group" of the British Psychoanalytical Society (the...
S2CID 56322745. Thurston, William P. (1982). "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry". Bulletin of the American Mathematical...
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