Calvaruso, G.; Tondeur, Ph.; Vanhecke, Lieven Four-dimensional ball-homogeneous and \(C\)-spaces. (English) Zbl 0884.53037 Beitr. Algebra Geom. 38, No. 2, 325-336 (1997). 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. Reviewer: Oldřich Kowalski (Praha) Cited in 4 Documents MSC: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C30 Differential geometry of homogeneous manifolds 53C35 Differential geometry of symmetric spaces Keywords:4-manifolds; \(C\)-space; ball-homogeneous space; Einstein space PDF BibTeX XML Cite \textit{G. Calvaruso} et al., Beitr. Algebra Geom. 38, No. 2, 325--336 (1997; Zbl 0884.53037) Full Text: EuDML EMIS OpenURL