Four-dimensional ball-homogeneous and \(C\)-spaces
A ball-homogeneous space is a Riemannian manifold on which the volume of a small geodesic ball depends only on the radius. A \(C\)-space is a Riemannian manifold on which the Jacobi operator along each geodesic has constant eigenvalues. We select here two of the main results: (1) A ball-homogeneous four-dimensional Hermitian Einstein space is locally symmetric. (2) A four-dimensional compact Hermitian Einstein \(C\)-space is locally symmetric.
scientific article; zbMATH DE number 1066113