Topology and a lorentz-invariant pseudo-riemannian metric of the manifold of directions in the physical space

In the mathematical model of the special relativity theory, a two-dimensional Minkowski subspace is treated as a one-dimensional direction in the physical space. The manifold of such planes is naturally endowed with the structure of a pseudo-Riemannian manifold on which the group of isochronous Lorentz transformations acts transitively by isometries. In this paper, the topology and the metric geometry of this manifold are studied. Bibliography: 4 titles. Translated from Zapiski Nauchnykh Seminar POMI, Vol. 246, 1997, pp. 141–151. Translated by S. Yu. Pilyugin.