A metric space of directions in Minkowski space (Q1882442)

Recently the author has introduced a new angular measure in \(d\)-dimensional Minkowski space [ibid. 80, No. 1--2, 31--47 (2004; Zbl 1068.51001)]. It determines the length of rectifiable curves on the \((d- 1)\)-dimensional topological sphere \(S\) that is the boundary of the convex set that serves as unit ball. Hence a Finsler metric is established on \(S\). The paper deals with some properties of this metric space. In particular it shows that \(\text{diam\,}S\leq\sqrt{2}\pi\).