A metric space of directions in Minkowski space

Abstract.

A new angular measure in a d-dimensional Minkowski space M was introduced recently. It determines the lengths of rectifiable curves in the (d - 1)-dimensional topological sphere S of all directions in M. Thus, a length structure appears on S. This results in the appropriate intrinsic metric in S. The paper deals with some properties of the length structure and the resulting metric space S. In particular, it shows that diam S ≤ √ 2 π.