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On Causal Characterization of Spherical Indicatrices of Timelike Curves in Minkowski 3-Space

Yıl 2020, Cilt: 2 Sayı: 2, 26 - 37, 09.12.2020

Öz

The aim of this paper is to discuss the causal characterization of spherical indicatrices of timelike curves in Minkowski 3-space. Firstly, we focus on the introduction of curves in Minkowski 3-space with its Frenet equations. In the next section the concept of spherical indicatrix of tangent, normal and binormal vectors of timelike curves is provided structurally with their casual properties. In addition, numerical example is provided in the last section.

Kaynakça

  • [1] Ali, A. T., (2009). New Spherical Curves and Their Spherical Indicatrices. Global Journal of Advance Research on Classical and Modern Geometries, 2(1), 28-38.
  • [2] Lipschutz, M. M. (1969). Schaum's Outline of Differential Geometry, McGraw-Hill, Canada.
  • [3] Lopez, R., (2014). Differential Geometry of Curves and Surface in Lorentz-Minkowski Space. International Electronic Journal of Geometry, 7(1), 44-107.
  • [4] Mohajan, H. K., (2013). Minkowski Geometry and Space-time Manifold in Relativity. Journal of Environmental Treatment Techniques, 1 (2), 101-109.
  • [5] O'neill, B.(1983). Semi-Riemannian geometry and its application to relativity, Academic press, New York.
  • [6] Samanci, H. K., Kalkan, O., & Celik, S., (2019). The Timelike Bezier Spline in Minkowski 3-Space. Journal of Science and Arts, 19(2), 357-374.
  • [7] Chung, S. K., (1982). A Study on The Spherical Indicatrix of Space Curve in $\mathbf{E}^3$. The Mathematical Education, 20(3), 23-26.
  • [8] Bilici, M., & Ali, A., (2017).On the Natural Lift Curves for the Involute Spherical Indicatrices in Minkowski 3-space. Malaya Journal of Matematik, 5(2), 407-415.
  • [9] Bilici, M., & Çalışkan, M. (2011). Some new notes on the involutes of the timelike curves in Minkowski 3-space. International Journal of Contemporary Mathematical Sciences, 6(41), 2019-2030.
  • [10] Bilici, M., & Çalışkan, M. (2019). Some New Results on The Curvatures of The Spherical Indicatrices of The Involutes of a Spacelike Curve with a Spacelike Binormal in Minkowski 3-space. MathLAB Journal, 2(1), 110-119.
  • [11] Philips, J. (1990). Freedom in Machinery, Screw Theory Exemplified, Cambridge University Press, Cambridge.
  • [12] Shikin, E.V. (1995). Handbook and Atlas of Curves, CRC Press, Florida.
  • [13] Rastogi, S. C. (1987). On quarter-symmetric metric connections. Tensor, 44(2), 133-141.
Yıl 2020, Cilt: 2 Sayı: 2, 26 - 37, 09.12.2020

Öz

Kaynakça

  • [1] Ali, A. T., (2009). New Spherical Curves and Their Spherical Indicatrices. Global Journal of Advance Research on Classical and Modern Geometries, 2(1), 28-38.
  • [2] Lipschutz, M. M. (1969). Schaum's Outline of Differential Geometry, McGraw-Hill, Canada.
  • [3] Lopez, R., (2014). Differential Geometry of Curves and Surface in Lorentz-Minkowski Space. International Electronic Journal of Geometry, 7(1), 44-107.
  • [4] Mohajan, H. K., (2013). Minkowski Geometry and Space-time Manifold in Relativity. Journal of Environmental Treatment Techniques, 1 (2), 101-109.
  • [5] O'neill, B.(1983). Semi-Riemannian geometry and its application to relativity, Academic press, New York.
  • [6] Samanci, H. K., Kalkan, O., & Celik, S., (2019). The Timelike Bezier Spline in Minkowski 3-Space. Journal of Science and Arts, 19(2), 357-374.
  • [7] Chung, S. K., (1982). A Study on The Spherical Indicatrix of Space Curve in $\mathbf{E}^3$. The Mathematical Education, 20(3), 23-26.
  • [8] Bilici, M., & Ali, A., (2017).On the Natural Lift Curves for the Involute Spherical Indicatrices in Minkowski 3-space. Malaya Journal of Matematik, 5(2), 407-415.
  • [9] Bilici, M., & Çalışkan, M. (2011). Some new notes on the involutes of the timelike curves in Minkowski 3-space. International Journal of Contemporary Mathematical Sciences, 6(41), 2019-2030.
  • [10] Bilici, M., & Çalışkan, M. (2019). Some New Results on The Curvatures of The Spherical Indicatrices of The Involutes of a Spacelike Curve with a Spacelike Binormal in Minkowski 3-space. MathLAB Journal, 2(1), 110-119.
  • [11] Philips, J. (1990). Freedom in Machinery, Screw Theory Exemplified, Cambridge University Press, Cambridge.
  • [12] Shikin, E.V. (1995). Handbook and Atlas of Curves, CRC Press, Florida.
  • [13] Rastogi, S. C. (1987). On quarter-symmetric metric connections. Tensor, 44(2), 133-141.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Arfah Arfah 0000-0002-7654-5520

Yayımlanma Tarihi 9 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 2 Sayı: 2

Kaynak Göster

APA Arfah, A. (2020). On Causal Characterization of Spherical Indicatrices of Timelike Curves in Minkowski 3-Space. Hagia Sophia Journal of Geometry, 2(2), 26-37.