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Dual Transformations in Galilean Spaces

Year 2020, , 52 - 61, 15.10.2020
https://doi.org/10.36890/iejg.683738

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........  .                                         ....................                                                                                                                   .

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.
Year 2020, , 52 - 61, 15.10.2020
https://doi.org/10.36890/iejg.683738

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.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Gülsüm Yüca 0000-0002-2015-7350

Yusuf Yaylı This is me 0000-0003-4398-3855

Publication Date October 15, 2020
Acceptance Date May 24, 2020
Published in Issue Year 2020

Cite

APA Yüca, G., & Yaylı, Y. (2020). Dual Transformations in Galilean Spaces. International Electronic Journal of Geometry, 13(2), 52-61. https://doi.org/10.36890/iejg.683738
AMA Yüca G, Yaylı Y. Dual Transformations in Galilean Spaces. Int. Electron. J. Geom. October 2020;13(2):52-61. doi:10.36890/iejg.683738
Chicago Yüca, Gülsüm, and Yusuf Yaylı. “Dual Transformations in Galilean Spaces”. International Electronic Journal of Geometry 13, no. 2 (October 2020): 52-61. https://doi.org/10.36890/iejg.683738.
EndNote Yüca G, Yaylı Y (October 1, 2020) Dual Transformations in Galilean Spaces. International Electronic Journal of Geometry 13 2 52–61.
IEEE G. Yüca and Y. Yaylı, “Dual Transformations in Galilean Spaces”, Int. Electron. J. Geom., vol. 13, no. 2, pp. 52–61, 2020, doi: 10.36890/iejg.683738.
ISNAD Yüca, Gülsüm - Yaylı, Yusuf. “Dual Transformations in Galilean Spaces”. International Electronic Journal of Geometry 13/2 (October 2020), 52-61. https://doi.org/10.36890/iejg.683738.
JAMA Yüca G, Yaylı Y. Dual Transformations in Galilean Spaces. Int. Electron. J. Geom. 2020;13:52–61.
MLA Yüca, Gülsüm and Yusuf Yaylı. “Dual Transformations in Galilean Spaces”. International Electronic Journal of Geometry, vol. 13, no. 2, 2020, pp. 52-61, doi:10.36890/iejg.683738.
Vancouver Yüca G, Yaylı Y. Dual Transformations in Galilean Spaces. Int. Electron. J. Geom. 2020;13(2):52-61.