Model Spaces in Riemannian and Sub-Riemannian Geometries

Abstract

The development of Riemannian geometry has been highly influenced by certain spaces with maximal symmetry called model spaces. Following in the footsteps of Klein's Erlangen program, model spaces fit with the approach of investigating the symmetries of a geometric object to understand the object itself. This thesis examines model spaces in the sub-Riemannian setting. The scientific contribution of the thesis is the classification of all sub-Riemannian model spaces with step and rank three.