Open Access
2013 Vector Parameters in Classical Hyperbolic Geometry
Danail Brezov, Clementina Mladenova, Ivaïlo Mladenov
J. Geom. Symmetry Phys. 30: 19-48 (2013). DOI: 10.7546/jgsp-30-2013-19-48


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.


Download Citation

Danail Brezov. Clementina Mladenova. Ivaïlo Mladenov. "Vector Parameters in Classical Hyperbolic Geometry." J. Geom. Symmetry Phys. 30 19 - 48, 2013.


Published: 2013
First available in Project Euclid: 26 May 2017

zbMATH: 1369.51004
MathSciNet: MR3113659
Digital Object Identifier: 10.7546/jgsp-30-2013-19-48

Rights: Copyright © 2013 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

Back to Top