Proceedings of the International Conference on Geometry, Integrability and Quantization

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

Dates
First available in Project Euclid: 13 July 2015

https://projecteuclid.org/ euclid.pgiq/1436815703

Digital Object Identifier
doi:10.7546/giq-15-2014-79-105

Mathematical Reviews number (MathSciNet)
MR3287750

Zentralblatt MATH identifier
1369.51005

Citation

Brezov, Danail S.; Mladenova, Clementina D.; Mladenov, Ivaïlo M. Vector Parameters in Classical Hyperbolic Geometry. Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, 79--105, Avangard Prima, Sofia, Bulgaria, 2014. doi:10.7546/giq-15-2014-79-105. https://projecteuclid.org/euclid.pgiq/1436815703