Special Ball-Homogeneous Spaces

Abstract

We continue the study of ball-homogeneous Riemannian manifolds, that is, R.ie-mannian spaces such that the volume of all sufficiently small geodesic balls or spheres only depends on the radius. First, we consider the case of locally reducible spaces. Then we treat the three-dimensional case, in particular for Einstein-like metrics and finally, we study confor-mally flat ball-homogeneous spaces. Our aim is to provide more partial answers to the question whether a ball-homogeneous space is locally homogeneous or not.