On Chapter Xii in Cartan's "LeÇONS Sur la GÉOMÉTRIE Des Espaces De Riemann"

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.