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On Evolutes of Null Cartan Curves in Minkowski 4-Space

Year 2021, Issue: 34, 37 - 44, 30.03.2021

Abstract

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.

References

  • 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.
Year 2021, Issue: 34, 37 - 44, 30.03.2021

Abstract

References

  • 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.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences, Applied Mathematics
Journal Section Research Article
Authors

Arfah Arfah 0000-0002-7654-5520

Publication Date March 30, 2021
Submission Date December 7, 2020
Published in Issue Year 2021 Issue: 34

Cite

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. March 2021;(34):37-44.
Chicago Arfah, Arfah. “On Evolutes of Null Cartan Curves in Minkowski 4-Space”. Journal of New Theory, no. 34 (March 2021): 37-44.
EndNote Arfah A (March 1, 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, no. 34, pp. 37–44, March 2021.
ISNAD Arfah, Arfah. “On Evolutes of Null Cartan Curves in Minkowski 4-Space”. Journal of New Theory 34 (March 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, no. 34, 2021, pp. 37-44.
Vancouver Arfah A. On Evolutes of Null Cartan Curves in Minkowski 4-Space. JNT. 2021(34):37-44.


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