Heintze Groups and Their Visual Boundaries
摘要
In this chapter, we show that to every Riemannian symmetric space of rank one and noncompact type, one can associate a ‘visual boundary’ that has the structure of a Carnot group. Visual boundaries are associated with spaces with negative sectional curvature. In fact, every homogeneous negatively curved manifold has the structure of a semi-direct product of the form \(N\rtimes {\mathbb R}\) for some positively graded nilpotent group N, which canonically represents the visual boundary. Hence, these boundaries are equipped with the structure of metric Lie groups that admit dilations.