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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 11, Pages 48–59 (Mi ivm1776)  
This article is cited in 5 scientific papers (total in 5 papers)

Projective geometry and the theory of physical structures

V. A. Kyrov

Gorno-Altaisk State University, Gorno-Altaisk, Russia
Full-text PDF (205 kB) Citations (5)
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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.
Keywords: physical structure, projective geometry.
Received: 04.07.2005
Revised: 05.04.2007
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, Volume 52, Issue 11, Pages 42–52
DOI: https://doi.org/10.3103/S1066369X08110054
Bibliographic databases:
UDC: 514.14
Language: Russian
Citation: V. A. Kyrov, “Projective geometry and the theory of physical structures”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 11, 48–59; Russian Math. (Iz. VUZ), 52:11 (2008), 42–52
Citation in format AMSBIB
\Bibitem{Kyr08}
\by V.~A.~Kyrov
\paper Projective geometry and the theory of physical structures
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 11
\pages 48--59
\mathnet{http://mi.mathnet.ru/ivm1776}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2530584}
\zmath{https://zbmath.org/?q=an:1167.22005|1160.81308}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 11
\pages 42--52
\crossref{https://doi.org/10.3103/S1066369X08110054}
Linking options:
  • https://www.mathnet.ru/eng/ivm1776
  • https://www.mathnet.ru/eng/ivm/y2008/i11/p48
    • This publication is cited in the following 5 articles:
    1. V. A. Kyrov, “Multiply Transitive Lie Group of Transformations as a Physical Structure”, Sib. Adv. Math., 32:2 (2022), 129  crossref
    2. V. A. Kyrov, “Kratno tranzitivnaya gruppa Li preobrazovanii kak fizicheskaya struktura”, Matem. tr., 24:2 (2021), 81–104  mathnet  crossref
    3. Vladimir A. Kyrov, “Commutative hypercomplex numbers and the geometry of two sets”, Zhurn. SFU. Ser. Matem. i fiz., 13:3 (2020), 373–382  mathnet  crossref
    4. V. A. Kyrov, “O vlozhenii dvumetricheskikh fenomenologicheski simmetrichnykh geometrii”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2018, no. 56, 5–16  mathnet  crossref  elib
    5. G. G. Mikhailichenko, “Phenomenologically symmetric geometry of two sets of rank $(3,2)$”, Russian Math. (Iz. VUZ), 60:2 (2016), 40–45  mathnet  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Full-text PDF :119
    References:56
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