Rune Suhr: On the 4 dimensional naturally reductive homogeneous Riemannian manifolds

The naturally reductive homogeneous spaces are homogeneous Riemannian spaces, i.e. Riemannian manifolds with a transitive action of the isometry group, with a simple metric, which yields among other things a particularly simple expression for the curvature R(X,Y,Y,X). There exists complete classifications for the spaces in dimensions 3,4 and 5, and we will sketch the proof of the classification of the 4 dimensional spaces.