Monthly Archives: April 2017

Geodesics on the upper half-plane – Part 2 circles

Posted on 2017/04/27 by arkajad

In the last note Geodesics on the upper half-plane – Part 1 Killing vectors we verified that SL(2,R) transformations are isometries of the upper half-plane endowed with the Riemannian metric defined by the line element (1)   The corresponding scalar … Continue reading →

Posted in Hyperbolic geometry, SU(1,1) | 6 Comments

Geodesics on the upper half-plane – Part 1 Killing vectors

Posted on 2017/04/26 by arkajad

According to Wikipedia In differential geometry, a geodesic is a generalization of the notion of a “straight line” to “curved spaces”. … The first line in the online Encyclopedia of mathematics is similar The notion of a geodesic line (also: … Continue reading →

Posted in Hyperbolic geometry, SU(1,1), Uncategorized | 1 Comment

Conformally Euclidean geometry of the upper half-plane

Posted on 2017/04/25 by arkajad

In Deriving invariant hyperbolic Riemannian metric on the half-plane we have calculated the line element for the SL(2,R) invariant hyperbolic geometry on the upper half-plane: (1)   Using this formula we can easily calculate the length of any segment of … Continue reading →

Posted in Hyperbolic geometry, SU(1,1) | 10 Comments