Classifying 3- and 4-dimensional homogeneous Riemannian manifolds by Cartan triples

Victor Patrangenaru

Vol. 173 (1996), No. 2, 511–532

DOI: 10.2140/pjm.1996.173.511

Abstract

In this paper, we show how to use the method of Cartan triples (see V. Patrangenaru) in small dimensions.

We classify the 3-dimensional simply connected homogeneous Riemannian spaces, and the 4-dimensional simply connected homogeneous Riemannian spaces with 5-dimensional total isometry group. We show that the smallest dimension where locally homogeneous Riemannian manifolds that are not locally isometric to homogeneous Riemannian spaces exist, is 5.

Mathematical Subject Classification 2000

Primary: 53C30

Secondary: 57N10, 57N13

Milestones

Received: 10 February 1993

Published: 1 April 1996