Lie Grup Etkisi Altında Yörüngelerin Özellikleri

Yıl 2022, , 619 - 629, 25.12.2022

Bülent Karakaş , Fatih Tuğrul

https://doi.org/10.53433/yyufbed.1096374

Öz

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.

Anahtar Kelimeler

Lie grup, Lie grup etkisi, Yörünge

Properties of Orbits Under Lie Group Action

Öz

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.

Anahtar Kelimeler

Lie group, Lie group action, Orbit

Kaynakça

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• 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
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• Herman, R. (1975). Lie Groups: History, Frontiers And applications Volume I, Sophus Lie’s 1880 transformation group paper. Massachusetts, USA: Math Sci Press.
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• 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.