Structure of standard homogeneous Einstein manifolds with simple isotropy group. I (Q1358093)

Let \(M = G/H\) be the quotient space of a compact connected semisimple Lie group \(G\) by the closed subgroup \(H\). The normal homogeneous Riemannian metric, induced by a Killing form with opposite sign, is familiar and referred to as the standard metric of the space \(M\). The Ricci curvatures on marked directions are calculated with the help of of marked Dynkin diagrams using so-called Casimir constants. The main result is that the list of compact simply connected standard homogeneous spaces with simple isotropy group is essentially that presented by É. Cartan, O. Manturov, J. Wolf, M. Wang and W. Ziller. [For Part II, see the following review Zbl 0901.53035].