On Chapter Xii in Cartan's "LeÇONS Sur la GÉOMÉTRIE Des Espaces De Riemann"
arXiv:0904.1256
Abstract
One shows that Cartan's method of adapted frames in Chapter XII of his famous treatise of Riemannian geometry, leads to a classification theorem of homogeneous Riemannian manifolds. Examples of classification in 3D dimensions obtained by Cartan are given using this powerful method.