Journal of Geometry and Symmetry in Physics

Vector Parameters in Classical Hyperbolic Geometry

Danail Brezov, Clementina Mladenova, and Ivaïlo Mladenov

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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.

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

First available in Project Euclid: 26 May 2017

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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.

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