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
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 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 Dehn surgery — In mathematics, hyperbolic Dehn surgery is an operation by which one can obtain further hyperbolic 3 manifolds from a given cusped hyperbolic 3 manifold. Hyperbolic Dehn surgery exists only in dimension three and is one which distinguishes… … 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 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
Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… … 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
Hyperbolic-orthogonal — In mathematics, two points in the Cartesian plane are hyperbolically orthogonal if the slopes of their rays from the origin are reciprocal to one another.If the points are ( x , y ) and ( u , v ), then they are hyperbolically orthogonal if : y /… … Wikipedia
Weeks manifold — In mathematics, the Weeks manifold, sometimes called the Fomenko Matveev Weeks manifold, is a closed hyperbolic 3 manifold obtained by (5,2) and (5,1) Dehn surgeries on the Whitehead link. It has volume approximately equal to .9427... and has the … Wikipedia
