Category Archives: Hyperbolic geometry

Riemannian metrics – left, right and bi-invariant

Posted on 2017/05/09 by arkajad

The discussion in this post applies to Riemannian metrics on Lie groups in general, but we will concentrate on just one case in hand: SL(2,R). Let be a Lie group. Vectors tangent to paths in at identity form the Lie … Continue reading →

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

Riemannian metric on SL(2,R)- explicit formula

Posted on 2017/05/08 by arkajad

Riemannian metric is usually expressed through its metric tensor. For instance in Conformally Euclidean geometry of the upper half-plane we were discussing the SL(2,R) invariant Riemannian metric on the upper half-plane and came out with the formula: (1)   Riemannian … Continue reading →

Posted in Hyperbolic geometry, SU(1,1) | 5 Comments

Riemannian metric on SL(2,R)

Posted on 2017/05/07 by arkajad

Every Lie group is like a Universe. Now it is time for us to play with the cosmology of SL(2,R). In Real magic – space-time in Lie algebra we have already started this game – we have defined a natural … Continue reading →

Posted in Geometry, Hyperbolic geometry | 2 Comments