Dual Transformations in Galilean Spaces

Yıl 2020, Cilt: 13 Sayı: 2, 52 - 61, 15.10.2020

Gülsüm Yüca , Yusuf Yaylı

https://doi.org/10.36890/iejg.683738

Öz

In this study, we define a dual transformation between $G^{n}$ and $G^{n}_{1}$. We examine the invariance of the plane where the shear motion is acting in Galilean and pseudo-Galilean spaces. We define a dual transformation between $\widehat{G^{n}}$ and $\widehat{G^{n}_{1}}$ as well. We provide applications in $G^{3}$ and $G^{3}_{1}$. In addition to applications, we draw their figures in order to reinforce the visualization in both spaces........  .                                         ....................                                                                                                                   .

Anahtar Kelimeler

Dual transformation, Galilean space, pseudo-Galilean space, shear motion, one-parameter motions

Kaynakça

• [1] Tütüncü, E. E., : The Geometry of Motions in the Galile Spaces, Phd. Thesis, Ankara University Graduate School of Natural and AppliedSciences, 2009.
• [2] Dohi R., Maeda Y., Mori M., Yoshida H.: A dual transformation between $S\widehat{O}(n+1)$ and $S\widehat{O}(n,1)$ and its geometric applications, Linear Algebra and its Applications 432: (2010), 770-776.
• [3] Yüca G., Yaylı Y.: A dual transformation between $S\widehat{O}(3)$ and $S\widehat{O}(2,1)$ and its geometric applications, Proc. Natl. Acad. Sci., India, Sect.A. Phys. Sci. 88-2: (2018) 267-273.
• [4] Yüca G.: Kinematics Applications of Dual Transformations, manuscript submitted for publication, 2020.
• [5] López R.: Differential geometry of curves and surfaces in Lorentz-Minkowski space, arXiv:0810.3351v1 [math.DG] 2008.
• [6] O’Neill B.: Semi-Riemannian Geometry, Pure and Applied Mathematics, 103,Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York (1983).
• [7] Yaylı Y., Çalışkan A., Uğurlu H.H.: The E. Study maps of circles on dual hyperbolic and Lorentzian unit spheres $H_{0}^{2}$ and $S_{1}^{2}$, Math. Proc. R. Ir. Acad. 102A-1: (2002) 37-47.