hyperbolic space


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hyperbolic space

[¦hī·pər¦bäl·ik ′spās]
(mathematics)
A space described by hyperbolic rather than cartesian coordinates.
References in periodicals archive ?
Goldman and colleagues consider moduli spaces of actions of discrete groups on hyperbolic space. Spaces of PSL(2,C)-representatives of fundamental groups of surfaces of negative Euler characteristic are natural objects upon which mapping class groups and related automorphism groups act, they say, and arise as deformation spaces of (possibly singular) locally homogeneous geometric structures on surfaces.
Particularly interesting classes of real Finsler metric spaces are Hilbert's metric spaces, which are natural generalisations of Klein's model of real hyperbolic space, and Thompson's metric on cones.
In particular, in Section 3, we study some existence results in partially ordered hyperbolic space for this class of nonexpansive type mapping and some illustrative nontrivial examples have also been discussed.
Details for background material on complex hyperbolic space will be found in [2].
In [1], Kohlenbach defined hyperbolic space in his paper titled "Some Logical Metatheorems with Applications in Functional Analysis, Transactions of the American Mathematical Society, Vol.
Let X be a Euclidean space [R.sup.d] or a hyperbolic space [H.sup.d].
Coral is an apt analogy, because Peled's core forms approximate hyperbolic space, a geometrical solution to maximise surface area within a limited volume.
Su: Hypersurfaces with constant scalar curvature in a hyperbolic space form, Balkan J.
In this section, we give as a table different Smarandache curves on de Sitter space or on hyperbolic space for spacelike curves in Minkowski-space.
These co-founders of non-Euclidean geometry proposed, independently of each other, a 2-body problem in hyperbolic space for which the attraction is proportional to the area of the sphere of radius equal to the hyperbolic distance between the bodies.
In particular Lopez [6] proved that the only minimal translation surfaces in hyperbolic space are totally geodesic planes.
Some topics discussed include singularities and self-similarities in gravitational collapse, horospherical geometry in the hyperbolic space, superconformal field theory and operator algebras, and quantum Birkhoff normal forms and semiclassical analysis.