Geometry of umbrella matrices in Galilean space

Çarboǧa M., YAYLI Y.

International Journal of Geometric Methods in Modern Physics, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1142/s0219887825501026
  • Dergi Adı: International Journal of Geometric Methods in Modern Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Galilean space, Galilean transformation, Lie algebras, Lie groups, umbrella matrices
  • Ankara Üniversitesi Adresli: Evet

Özet

In this study, we examine the Umbrella matrix group in Galilean space, which possesses the stochastic matrix property (i.e. leaves the 1 = [1 1]T ∈Rn axis fixed) within matrix groups. In our examination, we first obtain the matrix Lie group and Lie algebra in G3 space and then generalize this result. Furthermore, we present the Cayley formula, which gives the transition between the SO(n) Lie group and Lie algebra, for the first time between the Galilean Umbrella matrix Lie group and Lie algebra. Then, we define a case of shear motion along the 1 axis with the help of a special Galilean transformation and generate rotated surfaces in Galilean space using certain curves.