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Lie Grup Etkisi Altında Yörüngelerin Özellikleri

Year 2022, , 619 - 629, 25.12.2022
https://doi.org/10.53433/yyufbed.1096374

Abstract

Bu çalışmada, Lie grubunun manifold yapısının geometrik formu ile Lie dönüşüm grubu olarak diferensiyellenebilir bir manifoldun noktalarına etki ettirildiğinde, Lie grubunun geometrik yapısı ile Lie dönüşüm grubu etkisi altındaki noktaların yörüngelerinin geometrik yapıları arasındaki ilişkiler incelendi. Matlab uygulamaları yapıldı.

References

  • Brickell, F., & Clark, R. S. (1970). Diferentiable Manifolds. London, UK: Van Nostrand Reinhold Company Ltd.
  • Castillo, G. F. (2010). Differentiable Manifolds, A theoreetical physics approach. London, UK: Birkhäuser Cham. doi: 10.1007/978-3-030-45193-6
  • Gasparim, E., Grama, L., & San Martin, L. A. B. S. (2017). Adjoint orbits of semi-simple Lie groups and Langrangian submanifolds. Proceedings of the Edinburgh Mathematical Society, 60, 361–385. doi: 10.1017/S0013091516000286
  • Helgason, S. (1992). Sophus Lie, the mathematican, chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/viewer.html?pdfurl=https%3A%2F%2Fmath.mit.edu%2F~helgason%2Fsophus-lie.pdf&clen=1253215&chunk=true.pdf Erişim tarihi: 17.02.2022.
  • Herman, R. (1975). Lie Groups: History, Frontiers And applications Volume I, Sophus Lie’s 1880 transformation group paper. Massachusetts, USA: Math Sci Press.
  • Lovett, E. O. (1897). Sophus Lie’s transformation groups. The American Mathematical Monthly, 4, 237-242. doi: 10.1080/00029890.1898.11999787.
  • Kobayashi, S., & Nomizu, K. (1963). Foundations of Differential Geometry, John Wiley & Sons, New-York, London.
  • Tuğrul, F. (2016). Reflection to orbit submanifolds with acting Lie subgroup of properties of Lie subgroups. (MSc), Yuzuncu Yıl University, Institute of Natural and Applied Science, Van, Türkiye.

Properties of Orbits Under Lie Group Action

Year 2022, , 619 - 629, 25.12.2022
https://doi.org/10.53433/yyufbed.1096374

Abstract

In this study, the relationships between the geometrical structure of the Lie group and the geometric structures of the orbits of the points under the action of the Lie transformation group, when the geometric form of the manifold structure of the Lie group is acted upon on the points of a differentiable manifold as the Lie transform group are investigated. Matlab applications are made.

References

  • Brickell, F., & Clark, R. S. (1970). Diferentiable Manifolds. London, UK: Van Nostrand Reinhold Company Ltd.
  • Castillo, G. F. (2010). Differentiable Manifolds, A theoreetical physics approach. London, UK: Birkhäuser Cham. doi: 10.1007/978-3-030-45193-6
  • Gasparim, E., Grama, L., & San Martin, L. A. B. S. (2017). Adjoint orbits of semi-simple Lie groups and Langrangian submanifolds. Proceedings of the Edinburgh Mathematical Society, 60, 361–385. doi: 10.1017/S0013091516000286
  • Helgason, S. (1992). Sophus Lie, the mathematican, chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/viewer.html?pdfurl=https%3A%2F%2Fmath.mit.edu%2F~helgason%2Fsophus-lie.pdf&clen=1253215&chunk=true.pdf Erişim tarihi: 17.02.2022.
  • Herman, R. (1975). Lie Groups: History, Frontiers And applications Volume I, Sophus Lie’s 1880 transformation group paper. Massachusetts, USA: Math Sci Press.
  • Lovett, E. O. (1897). Sophus Lie’s transformation groups. The American Mathematical Monthly, 4, 237-242. doi: 10.1080/00029890.1898.11999787.
  • Kobayashi, S., & Nomizu, K. (1963). Foundations of Differential Geometry, John Wiley & Sons, New-York, London.
  • Tuğrul, F. (2016). Reflection to orbit submanifolds with acting Lie subgroup of properties of Lie subgroups. (MSc), Yuzuncu Yıl University, Institute of Natural and Applied Science, Van, Türkiye.
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Details

Primary Language Turkish
Journal Section Articles
Authors

Bülent Karakaş 0000-0002-3915-6526

Fatih Tuğrul 0000-0003-0967-5103

Publication Date December 25, 2022
Submission Date March 31, 2022
Published in Issue Year 2022

Cite

APA Karakaş, B., & Tuğrul, F. (2022). Lie Grup Etkisi Altında Yörüngelerin Özellikleri. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 27(3), 619-629. https://doi.org/10.53433/yyufbed.1096374