Topology and a lorentz-invariant pseudo-riemannian metric of the manifold of directions in the physical space
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Abstract
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.
Keywords
Manifold Physical Space Plane Versus Inertial Particle Grassmann Manifold
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References
- 1.R. I. Pimenov, “Spaces of kinematic type (mathematical theory of time-space),” Zap. Nauchn. Semin. LOMI, 6, 1–496 (1968).Google Scholar
- 2.S. E. Kozlov, Mathematical Foundations of Special Relativity theory and Lobachevski Space [in Russian], Saint Petersburg State Univ., Saint Petersburg (1995).Google Scholar
- 3.S. E. Kozlov, “Geometry of real Grassmann manifolds. Parts I, II,” Zap. Nauchn. Semin. POMI, 246, 84–107 (1997).Google Scholar
- 4.Yu. D. Burago and V. A. Zalgaller, Introduction to Riemannian Geometry [in Russian], Nauka, Saint Petersburg (1994).MATHGoogle Scholar
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© Kluwer Academic/Plenum Publishers 2000