Abstract
In this paper, we establish connection between s-metric physical structures of rank (s + 3, 2) and projective geometry. In particular, we find explicit functional relations determining phenomenological symmetry. For s = 1, this relation is expressed in terms of the anharmonic ratio of four points. We prove that these functional relations lead to the group of projective transformations.
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References
G. G. Mikhailichenko, “Two-metric Physical Structures of Rank (n + 1, 2),” Sib. Matem. Zhurn. 34(3), 132–143 (1993).
G. G. Mikhailichenko, Group Symmetry of Physical Structures Barnaul-Gorno-Altaisk, 2003 [in Russian].
N. V. Efimov, Higher Geometry (GIFML, Moscow, 1961) [in Russian].
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Original Russian Text © V.A. Kyrov, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 11, pp. 48–59.
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Kyrov, V.A. Projective geometry and the theory of physical structures. Russ Math. 52, 42–52 (2008). https://doi.org/10.3103/S1066369X08110054
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DOI: https://doi.org/10.3103/S1066369X08110054