Structure of standard homogeneous Einstein manifolds with simple isotropy group. II
[For Part I, see the preceding review Zbl 0901.53034.] The metrics of standard homogeneous Riemannian manifolds are determined with the help of Killing forms on the group of motions of this space. First, the author discusses the question whether a standard homogeneous Riemannian manifold is Einstein. The author also builds new nontrivial examples of homogeneous manifolds with a semisimple group of motions and also with a semisimple isotropy group. The existence of these spaces depends on the existence of solutions to some diophantine equations which are found by direct substitution.
standard homogeneous Riemannian manifolds
scientific article; zbMATH DE number 1023952