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 consequence of the work of William Thurston, it is known that every knot is precisely one of the following: hyperbolic, a torus knot, or a satellite knot. As a consequence, hyperbolic knots can be considered plentiful. A similar heuristic applies to hyperbolic links.
As a consequence of Thurston's hyperbolic Dehn surgery theorem, performing Dehn surgeries on a hyperbolic link enables one to obtain many more hyperbolic 3-manifolds.
hyperboliclink is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic...
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just...
knot theory, the hyperbolic volume of a hyperboliclink is the volume of the link's complement with respect to its complete hyperbolic metric. The volume...
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...
Look up hyperbolic in Wiktionary, the free dictionary. Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve)...
can be proved to be linked by counting their Fox n-colorings. As links, they are Brunnian, alternating, algebraic, and hyperbolic. In arithmetic topology...
In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension. They are especially studied in...
In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three...
Mostow–Prasad rigidity, the hyperbolic structure on the complement of a hyperboliclink is unique, which means the hyperbolic volume is an invariant for...
In mathematics, hyperbolic trigonometry can mean: The study of hyperbolic triangles in hyperbolic geometry (traditional trigonometry is the study of triangles...
n > 1 there exists a hyperboliclink of n components such that any proper sublink is an unlink (a Brunnian link). The Whitehead link and Borromean rings...
A hyperbolic tree (often shortened as hypertree) is an information visualization and graph drawing method inspired by hyperbolic geometry. Displaying hierarchical...
plane parallel to the axis of symmetry is a parabola. The paraboloid is hyperbolic if every other plane section is either a hyperbola, or two crossing lines...
Other hyperbolic invariants include the shape of the fundamental parallelogram, length of shortest geodesic, and volume. Modern knot and link tabulation...
hyperbolic Dehn surgery is an operation by which one can obtain further hyperbolic 3-manifolds from a given cusped hyperbolic 3-manifold. Hyperbolic Dehn...
In astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit is the trajectory of any object around a central body with more than...
Hyperbolic theory may refer to: Hyperbolic geometry The theory of hyperbolic partial differential equations This disambiguation page lists mathematics...
the minimum-volume hyperbolic manifolds with one cusp and the minimum-volume hyperbolic manifold with no cusps. The Whitehead link is named for J. H....
the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number...
In mathematics, a hyperbolic point is a certain kind of point, one of: A point in a hyperbolic geometry A point of negative Gaussian curvature on a smooth...
In hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic...
the Hopf link is R × S1 × S1, the cylinder over a torus. This space has a locally Euclidean geometry, so the Hopf link is not a hyperboliclink. The knot...
The Soboleva modified hyperbolic tangent, also known as (parametric) Soboleva modified hyperbolic tangent activation function ([P]SMHTAF), is a special...
-links, hyperbolic Brunnian links, and hyperbolic Brunnian links in unlink-complements, the last of which can be further reduced into a Brunnian link in 3-sphere...
Hyperbolic structure may refer to: Hyperboloid structure Hyperbolic set This disambiguation page lists mathematics articles associated with the same title...
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