Generalization of the Cayley transform in 3D homogeneous geometries

Authors : Zlatko Erjavec

Pages : 2942-2952

View : 10 | Download : 4

Publication Date : 9999-12-31

Article Type : Makaleler

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.
Keywords : Cayley transform, homogeneous geometry, isometry