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hyperbolic metric

См. также в других словарях:

  • Hyperbolic volume (knot) — In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is simply the volume of the link s complement with respect to its complete hyperbolic metric. The volume is necessarily finite. The hyperbolic volume of a non… …   Wikipedia

  • hyperbolic plane — noun A topological space homeomorphic to a plane (or open disk) and equipped with a hyperbolic metric …   Wiktionary

  • Hyperbolic group — In group theory, a hyperbolic group, also known as a word hyperbolic group, Gromov hyperbolic group, negatively curved group is a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic… …   Wikipedia

  • Hyperbolic geometry — Lines through a given point P and asymptotic to line R. A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparall …   Wikipedia

  • Hyperbolic space — In mathematics, hyperbolic n space, denoted H n , is the maximally symmetric, simply connected, n dimensional Riemannian manifold with constant sectional curvature −1. Hyperbolic space is the principal example of a space exhibiting hyperbolic… …   Wikipedia

  • Hyperbolic set — In mathematics, a subset of a manifold is said to have hyperbolic structure with rspect to a map f , when its tangent bundle may be split into two invariant subbundles, one of which is contracting, and the other expanding with respect to f .… …   Wikipedia

  • Hyperbolic motion — In geometry, a hyperbolic motion is a mapping of a model of hyperbolic geometry that preserves the distance measure in the model. Such a mapping is analogous to congruences of Euclidean geometry which are compositions of rotations and… …   Wikipedia

  • Hyperbolic 3-manifold — A hyperbolic 3 manifold is a 3 manifold equipped with a complete Riemannian metric of constant sectional curvature 1. In other words, it is the quotient of three dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely… …   Wikipedia

  • Metric space — In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3 dimensional Euclidean… …   Wikipedia

  • Hyperbolic link — In mathematics, a hyperbolic link is a link in the 3 sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry. A hyperbolic knot is a hyperbolic link with one component.As a… …   Wikipedia

  • Poincaré metric — In mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two dimensional surface of constant negative curvature. It is the natural metric commonly used in a variety of calculations in hyperbolic geometry… …   Wikipedia

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