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(7n-1)-Boyutlu Projektif Uzayda Fano Düzlemleri Üzerine

Year 2022, , 442 - 447, 31.08.2022
https://doi.org/10.18185/erzifbed.982509

Abstract

Bu çalışmada, (n:k)-SCID kullanarak (7n-1)-boyutlu P projektif uzayında noktaları P nin (n-1)-boyutlu alt uzayları ve doğruları P nin (3n-1)-boyutlu alt uzayları olan Fano düzlemleri elde ediyoruz. de noktaları noktalar ve doğruları düzlemler olan ve de noktaları doğrular ve doğruları 5-uzaylar olan Fano düzlemlerinin örneklerini veriyoruz.

References

  • Adamson, I. T. (1964). Introduction to field theory. Edinburgh: Oliver and Boyd.
  • Akça, Z., Bayar, A., Ekmekçi, S., Kaya, R., 2010, Bazı Geometrilerin Sonlu Projektif Uzaylara Gömülmeleri Üzerine, Tübitak Proje No: 108T340.
  • Akça, Z., Bayar, A., Ekmekçi, S., 4. Mertebeden Projektif Düzlemin 4-boyutlu Projektif Uzaya Gömülmesi Üzerine, Ogü Bap Proje No: 201619D38, 2017.
  • Artin, E. (1948). Galois theory. Notre Dame: University of Notre Dame Press
  • Cullinane, H., 2007, The Klein Correspondence, Penrose Space-Time, and a Finite Model, http://finitegeometry.org/sc/64/KleinCorr.html
  • Dorje, C., Brody, L.P., 2014, Twistor cosmology and quantum space-time, arXiv:hep-th/0502218v1.
  • Ekmekçi, S., Bayar, A., Akça, Z., 2017, PG(4,4) Projektif Uzayındaki Projektif Düzlemler Üzerine, Ogü Bap Proje No: 201619D37 .
  • Gokhan, S., Demirci, M., Ikikardes, N. Y., & Cangul, I. N., 2007. Rational Points on Elliptic Curves y²=x³+a³ in F_{p}, where p≡5 (mod6) is Prime. International Journal of Mathematics Sciences, 1(4), 247 - 250.
  • Hirschfeld, J. A. Thas., 2016, General Galois Geometries, Springer Monongraphs in Mathematics.
  • Klein, F.,1868, Über die Transformation der allgemeinen Gleichung des zweiten Grades zwischen Linien-Koordinaten auf eine kanonische Form, Math., p. 539-578
  • Penttila, T., Siciliano A., 2015 On collineation groups of finite projective spaces containing a Singer cycle, Journal of Geometry 107(3).
  • Plücker, J., 1865, On a New Geometry of Space, Philosophical Transactions of the Royal Society of London, Vol. 155, pp. 725-791.

On The Fano Planes in (7n-1)-dimensional Projective Spaces

Year 2022, , 442 - 447, 31.08.2022
https://doi.org/10.18185/erzifbed.982509

Abstract

In this study, we obtain Fano planes whose points are (n-1)-dimensional subspaces and lines are (3n-1)-
dimensional subspaces of P in (7n-1)-dimensional projective space P ,using (n;k)-SCID. We give examples
of Fano planes whose the lines of Fano configuration are planes and the points are points of
PG(6,2)
and the
lines of Fano configuration are 5-spaces and the points are lines of
PG(13,2).

References

  • Adamson, I. T. (1964). Introduction to field theory. Edinburgh: Oliver and Boyd.
  • Akça, Z., Bayar, A., Ekmekçi, S., Kaya, R., 2010, Bazı Geometrilerin Sonlu Projektif Uzaylara Gömülmeleri Üzerine, Tübitak Proje No: 108T340.
  • Akça, Z., Bayar, A., Ekmekçi, S., 4. Mertebeden Projektif Düzlemin 4-boyutlu Projektif Uzaya Gömülmesi Üzerine, Ogü Bap Proje No: 201619D38, 2017.
  • Artin, E. (1948). Galois theory. Notre Dame: University of Notre Dame Press
  • Cullinane, H., 2007, The Klein Correspondence, Penrose Space-Time, and a Finite Model, http://finitegeometry.org/sc/64/KleinCorr.html
  • Dorje, C., Brody, L.P., 2014, Twistor cosmology and quantum space-time, arXiv:hep-th/0502218v1.
  • Ekmekçi, S., Bayar, A., Akça, Z., 2017, PG(4,4) Projektif Uzayındaki Projektif Düzlemler Üzerine, Ogü Bap Proje No: 201619D37 .
  • Gokhan, S., Demirci, M., Ikikardes, N. Y., & Cangul, I. N., 2007. Rational Points on Elliptic Curves y²=x³+a³ in F_{p}, where p≡5 (mod6) is Prime. International Journal of Mathematics Sciences, 1(4), 247 - 250.
  • Hirschfeld, J. A. Thas., 2016, General Galois Geometries, Springer Monongraphs in Mathematics.
  • Klein, F.,1868, Über die Transformation der allgemeinen Gleichung des zweiten Grades zwischen Linien-Koordinaten auf eine kanonische Form, Math., p. 539-578
  • Penttila, T., Siciliano A., 2015 On collineation groups of finite projective spaces containing a Singer cycle, Journal of Geometry 107(3).
  • Plücker, J., 1865, On a New Geometry of Space, Philosophical Transactions of the Royal Society of London, Vol. 155, pp. 725-791.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Makaleler
Authors

Ziya Akça 0000-0001-6379-0546

Abdilkadir Altıntaş 0000-0002-7012-352X

Publication Date August 31, 2022
Published in Issue Year 2022

Cite

APA Akça, Z., & Altıntaş, A. (2022). On The Fano Planes in (7n-1)-dimensional Projective Spaces. Erzincan University Journal of Science and Technology, 15(2), 442-447. https://doi.org/10.18185/erzifbed.982509