A new weighted metric: the relative metric II

In the first part of this investigation we generalized a weighted distance function of R.-C. Li’s and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so-called M-relative metric are established. Specifically, isometries and quasiconvexity results are derived. We also illustrate connections between our approach and generalizations of the hyperbolic metric.  2004 Elsevier Inc. All rights reserved.