engleski

Isometry between two models of SL(2, R) geometry

Among eight 3-dimensional homogeneous geometries, "twisted" product geometries SL(2, R), Nil and Sol are specific because they are structured as line bundles over hyperbolic, Euclidean and pseudo-Euclidean plane, respectively. Among these geometries, the SL(2, R) is the least researched and generally, because of its features presents a rich area for future investigation. Currently, there are two models of SL(2, R) geometry: the hyperboloid model of SL(2, R) geometry and the upper half-plane model of SL(2, R) geometry. In this talk we prove that the hyperboloid model and the upper half-plane model of SL(2, R) geometry are isometric. Having in mind that there are results in both models which are not quite comparable this isometry gives us an opportunity for transferring some of known results between models.

SL(2, R) geometry, isometry, homogeneous space

nije evidentirano