Abstract
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........ . .................... .
Keywords
Dual transformation Galilean space pseudo-Galilean space shear motion one-parameter motions
References
- [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.
Abstract
References
- [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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | October 15, 2020 |
| Acceptance Date | May 24, 2020 |
| Published in Issue | Year 2020 Volume: 13 Issue: 2 |
