Four-dimensional ball-homogeneous and \(C\)-spaces. (English) Zbl 0884.53037

Calvaruso, G.; Tondeur, Ph.; Vanhecke, Lieven

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)

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