Hyperbolic space

In mathematics, hyperbolic n-space, denoted Hn, 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 geometry. It can be thought of as the negative curvature analogue of the n-sphere.

Related Topics:
Mathematics - Simply connected - Riemannian manifold - Sectional curvature - Hyperbolic geometry - Sphere

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In fact, every closed manifold of constant negative curvature −1 is isometric to the quotient space Hn/Γ where Γ is discrete group of isometries of Hn.

Related Topics:
Closed manifold - Isometric - Quotient space - Discrete group - Isometries

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Hyperbolic space is a homogeneous space.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Hyperbolic 2-space, H2, is also called the hyperbolic plane.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~