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On Evolutes of Null Cartan Curves in Minkowski 4-Space

Yıl 2021, Sayı: 34, 37 - 44, 30.03.2021

Arfah Arfah

Öz

This paper aims to discuss the theory of evolutes of null Cartan curves in Minkowski 4-space. In the second part, we present the basic concepts of curves in Minkowski 4-space with its Frenet equations. In the next section, the definition of evolutes of null Cartan curves in Minkowski 4-space is given, and we derive some theorems related to casual characters of those evolute curves. The last part provides an example for the theorems in the preceding section.

Anahtar Kelimeler

null Cartan curves Minkowski space Evolutes involutes

Kaynakça

  • U. C. Merzbach, C. B. Boyer, A History of Mathematics Third Edition, John Wiley and Sons Inc., 2010.
  • M. Bilici, M. Calışkan, On the Involutes of the space-like Curve with a time-like Binormal in Minkowski 3-space, International Mathematical Forum 4 (2009) 1497-1509.
  • B. Bukcu, M. K. Karacan, On the Involute and Evolute Curves of the time-like Curve in Minkowski 3-Space, Demonstratio Mathematica 40 (2007) 721-732.
  • B. Bukcu, M. K. Karacan, On Involute and Evolute Curves of space-like Curve with a space-like Principal Normal in Minkowski 3-space, International Journal of Mathematical Combinatorics 1 (2009) 27-37.
  • D. Fuchs, Evolutes and Involutes of Spatial Curves, The American Mathematical Monthly 120(3) (2013) 217-231.
  • M. M. Lipschutz, Schaum's Outline of Differential Geometry, McGraw-Hill, 1969.
  • U. Öztürk, E. B. K. Öztürk, K. İlarslan, On the Involute-Evolute of The Pseudonull Curve in Minkowski 3-Space, Journal of Applied Mathematics 6(10) (2013) 1-6.
  • T. Sochi, Introduction to Differential Geometry of Space Curves and Surfaces, CreateSpace Independent Publishing, 2017.
  • G. U. Kaymanlı, Characterization of the Evolute Offset of Ruled Surfaces with B-Darboux Frame, Journal of New Theory 33 (2020) 50-55.
  • M. Hanif, H. Z. Hua, E. Nesovic, On Involutes of Order k of a Null Cartan Curve in Minkowski Spaces, Filomat 33(8) 2295-2305.
  • A. Ferrandez, A. Gimenez, P. Lucas, Null Generalized Helices in Lorentz-Minkowski Spaces, Journal of Physics A General Physics 35(39) (2002) 8243-8251.
  • J. Inoguchi, S. Lee. Null Curves in Minkowski 3-Space, International Electronic Journal of Geometry 1(2) (2008) 40-83.
  • J. Qian, Y. H. Kim, Directional Associated Curves of a Null Curve in E^3_1, Bulletin of The Korean Mathematical Society 52(1) (2015) 183-200.
  • K. L. Duggal, D. H. Jin, Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  • H. K. Mohajan, Minkowski Geometry and Spacetime Manifold in Relativity, Journal of Environmental Techniques 1 (2013) 101-109.
  • S. Yılmaz, M. Turgut, Determination of Frenet Apparatus of Partially Null and Pseudo Null Curves in Minkowski Space-time, International Journal of Contemporary Mathematical Sciences 3(27) (2008) 1337-1341.
  • X. Liu, Z. Wang, On Lightlike Hypersurfaces and Lightlike Focal Sets of Null Cartan Curves in Lorentz-Minkowski Spacetime, Journal of Nonlinear Science and Application 8 (2015) 628-639.
  • M. Sasaki, Notes on Null Curve in Minkowski Spaces, Turkish Journal of Mathematics 34 (2010) 417-424.
  • A. C. Çöken, Ü. Çiftçi, On the Cartan Curvatures of a Null Curve in Minkowski Spacetime, Geometry Dedicata 114 (2005) 71-78.

Yıl 2021, Sayı: 34, 37 - 44, 30.03.2021

Arfah Arfah

Öz

Kaynakça

  • U. C. Merzbach, C. B. Boyer, A History of Mathematics Third Edition, John Wiley and Sons Inc., 2010.
  • M. Bilici, M. Calışkan, On the Involutes of the space-like Curve with a time-like Binormal in Minkowski 3-space, International Mathematical Forum 4 (2009) 1497-1509.
  • B. Bukcu, M. K. Karacan, On the Involute and Evolute Curves of the time-like Curve in Minkowski 3-Space, Demonstratio Mathematica 40 (2007) 721-732.
  • B. Bukcu, M. K. Karacan, On Involute and Evolute Curves of space-like Curve with a space-like Principal Normal in Minkowski 3-space, International Journal of Mathematical Combinatorics 1 (2009) 27-37.
  • D. Fuchs, Evolutes and Involutes of Spatial Curves, The American Mathematical Monthly 120(3) (2013) 217-231.
  • M. M. Lipschutz, Schaum's Outline of Differential Geometry, McGraw-Hill, 1969.
  • U. Öztürk, E. B. K. Öztürk, K. İlarslan, On the Involute-Evolute of The Pseudonull Curve in Minkowski 3-Space, Journal of Applied Mathematics 6(10) (2013) 1-6.
  • T. Sochi, Introduction to Differential Geometry of Space Curves and Surfaces, CreateSpace Independent Publishing, 2017.
  • G. U. Kaymanlı, Characterization of the Evolute Offset of Ruled Surfaces with B-Darboux Frame, Journal of New Theory 33 (2020) 50-55.
  • M. Hanif, H. Z. Hua, E. Nesovic, On Involutes of Order k of a Null Cartan Curve in Minkowski Spaces, Filomat 33(8) 2295-2305.
  • A. Ferrandez, A. Gimenez, P. Lucas, Null Generalized Helices in Lorentz-Minkowski Spaces, Journal of Physics A General Physics 35(39) (2002) 8243-8251.
  • J. Inoguchi, S. Lee. Null Curves in Minkowski 3-Space, International Electronic Journal of Geometry 1(2) (2008) 40-83.
  • J. Qian, Y. H. Kim, Directional Associated Curves of a Null Curve in E^3_1, Bulletin of The Korean Mathematical Society 52(1) (2015) 183-200.
  • K. L. Duggal, D. H. Jin, Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  • H. K. Mohajan, Minkowski Geometry and Spacetime Manifold in Relativity, Journal of Environmental Techniques 1 (2013) 101-109.
  • S. Yılmaz, M. Turgut, Determination of Frenet Apparatus of Partially Null and Pseudo Null Curves in Minkowski Space-time, International Journal of Contemporary Mathematical Sciences 3(27) (2008) 1337-1341.
  • X. Liu, Z. Wang, On Lightlike Hypersurfaces and Lightlike Focal Sets of Null Cartan Curves in Lorentz-Minkowski Spacetime, Journal of Nonlinear Science and Application 8 (2015) 628-639.
  • M. Sasaki, Notes on Null Curve in Minkowski Spaces, Turkish Journal of Mathematics 34 (2010) 417-424.
  • A. C. Çöken, Ü. Çiftçi, On the Cartan Curvatures of a Null Curve in Minkowski Spacetime, Geometry Dedicata 114 (2005) 71-78.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik, Uygulamalı Matematik
Bölüm Araştırma Makalesi
Yazarlar

Arfah Arfah 0000-0002-7654-5520

Yayımlanma Tarihi 30 Mart 2021
Gönderilme Tarihi 7 Aralık 2020
Yayımlandığı Sayı Yıl 2021 Sayı: 34

Kaynak Göster

APA Arfah, A. (2021). On Evolutes of Null Cartan Curves in Minkowski 4-Space. Journal of New Theory(34), 37-44.
AMA Arfah A. On Evolutes of Null Cartan Curves in Minkowski 4-Space. JNT. Mart 2021;(34):37-44.
Chicago Arfah, Arfah. “On Evolutes of Null Cartan Curves in Minkowski 4-Space”. Journal of New Theory, sy. 34 (Mart 2021): 37-44.
EndNote Arfah A (01 Mart 2021) On Evolutes of Null Cartan Curves in Minkowski 4-Space. Journal of New Theory 34 37–44.
IEEE A. Arfah, “On Evolutes of Null Cartan Curves in Minkowski 4-Space”, JNT, sy. 34, ss. 37–44, Mart 2021.
ISNAD Arfah, Arfah. “On Evolutes of Null Cartan Curves in Minkowski 4-Space”. Journal of New Theory 34 (Mart 2021), 37-44.
JAMA Arfah A. On Evolutes of Null Cartan Curves in Minkowski 4-Space. JNT. 2021;:37–44.
MLA Arfah, Arfah. “On Evolutes of Null Cartan Curves in Minkowski 4-Space”. Journal of New Theory, sy. 34, 2021, ss. 37-44.
Vancouver Arfah A. On Evolutes of Null Cartan Curves in Minkowski 4-Space. JNT. 2021(34):37-44.
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