de Sitter space

From Mathematics wiki

Jump to: navigation, search

Consider the n+1\,-dimensional Minkowski space \mathbb{R}^{1,n}\, with metric

ds^2 = -(dx^0)^2 + (dx^1)^2 + ... + (dx^n)^2\,

and embed into it the one-sheeted hyperboloid defined by

-(x^0)^2 + (x^1)^2 + ... (x^n)^2 = R^2\,.

This submanifold has codimension 1\, and is known as de Sitter space or \mathrm{dS}_n\,. The induced metric on \mathrm{dS}_n\, has Lorentzian signature.

See also anti de Sitter space.

Retrieved from "http://www.mathematics.thetangentbundle.net/wiki/de_Sitter_space"
Personal tools