Category Archives: Hyperbolic geometry

Minkowski patches in the Einstein universe

Posted on 2025/11/27 by arkajad

This post is a continuation of Floating in the Einstein Universe. Let us recall the relevant definition from the previous post.     . So is the union of all light rays through p. For we have only two light … Continue reading →

Posted in Compactified Minkowski space, Hyperbolic geometry, Uncategorized | Tagged , | Leave a comment

Becoming anti de Sitter

Posted on 2017/05/14 by arkajad

In the last post we were discussing Killing vector fields of the group SL(2,R). It was done without specifying any reason for doing it – except that it somehow came in our way naturally. But now there is an opportunity … Continue reading →

Posted in Geometry, Hyperbolic geometry, SU(1,1) | 2 Comments

SL(2,R) Killing vector fields in coordinates

Posted on 2017/05/11 by arkajad

In Parametrization of SL(2,R) we introduced global coordinates on the group SL(2,R). Any matrix in SL(2,R) can be uniquely written as (1)   If is the matrix with components then its coordinates can be expressed as functions of the matrix … Continue reading →

Posted in Hyperbolic geometry, Mathematica, SU(1,1) | 3 Comments