## Journal of Geometry and Symmetry in Physics

### Vector Parameters in Classical Hyperbolic Geometry

#### Abstract

Here we use an extension of Rodrigues' vector parameter construction for pseudo-rotations in order to obtain explicit formulae for the generalized Euler decomposition with arbitrary axes for the structure groups in the classical models of hyperbolic geometry. Although the construction is projected from the universal cover $\,\mathsf{SU}(1,1)\simeq\mathsf{SL}(2,\mathbb{R})$, most attention is paid to the $2+1$ Minkowski space model, following the close analogy with the Euclidean case, and various decompositions of the restricted Lorentz group $\mathsf{SO}^+(2,1)$ are investigated in detail. At the end we propose some possible applications in special relativity and scattering theory.

#### Article information

Source
J. Geom. Symmetry Phys., Volume 30 (2013), 19-48.

Dates
First available in Project Euclid: 26 May 2017

https://projecteuclid.org/euclid.jgsp/1495764079

Digital Object Identifier
doi:10.7546/jgsp-30-2013-19-48

Mathematical Reviews number (MathSciNet)
MR3113659

Zentralblatt MATH identifier
1369.51004

#### Citation

Brezov, Danail; Mladenova, Clementina; Mladenov, Ivaïlo. Vector Parameters in Classical Hyperbolic Geometry. J. Geom. Symmetry Phys. 30 (2013), 19--48. doi:10.7546/jgsp-30-2013-19-48. https://projecteuclid.org/euclid.jgsp/1495764079