Turkish Journal of Mathematics
Abstract
The Cayley transform maps the unit disk onto the upper half-plane, conformally and isometrically. In this paper, we generalize the Cayley transform in three-dimensional homogeneous geometries which are fiber bundles over the hyperbolic plane. Obtained generalizations are isometries between existing models in corresponding homogeneous geometries. Particularly, constructed isometry between two models of { $\widetilde{SL(2,\mathbb{R})}$} geometry is nontrivial and enables comparison and transfer of known and even future results between these two models.
DOI
10.3906/mat-1802-28
Keywords
Cayley transform, homogeneous geometry, isometry
First Page
2942
Last Page
2952
Recommended Citation
ERJAVEC, Z (2018). Generalization of the Cayley transform in 3D homogeneous geometries. Turkish Journal of Mathematics 42 (6): 2942-2952. https://doi.org/10.3906/mat-1802-28
