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Dergiler / International Electronic Journal of Geometry / 2020 / Volume: 13 Issue: 2

Dual Transformations in Galilean Spaces

Gülsüm Yüca(AKSARAY UNIVERSITY)0000-0002-2015-7350
Yusuf Yaylı(ANKARA UNIVERSITY)0000-0003-4398-3855
Sayfa
—
Yayın Tarihi
2020-10-15
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In addition to applications, we draw their figures in order to reinforce the visualization in both spaces. ....... . .................... .

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, we define a dual transformation between $G^{n}$ and $G^{n}_{1}$.
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Temel Bulgular & Veri:We define a dual transformation between $\widehat{G^{n}}$ and $\widehat{G^{n}_{1}}$ as well.
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Sonuç & Katkı:In addition to applications, we draw their figures in order to reinforce the visualization in both spaces. ....... . .................... .
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Dual transformation · Galilean space · pseudo-Galilean space

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

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Bu Makaleye Atıf Yap

Yüca, G., Yaylı, Y. (2020). Dual Transformations in Galilean Spaces. International Electronic Journal of Geometry, Volume: 13 Issue: 2. https://doi.org/10.36890/iejg.683738

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Kaynakça (8)

  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.
  8. Tütüncü, E. E.,: The Geometry of Motions in the Galile Spaces, Phd. Thesis, Ankara University Graduate School of Natural and AppliedSciences, 2009.