Year 2021, Volume , Issue 34, Pages 37 - 44 2021-03-30

On Evolutes of Null Cartan Curves in Minkowski 4-Space

Arfah ARFAH [1]


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.
null Cartan curves, Minkowski space, Evolutes, involutes
  • 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.
Primary Language en
Subjects Mathematics, Mathematics, Interdisciplinary Applications
Journal Section Research Article
Authors

Orcid: 0000-0002-7654-5520
Author: Arfah ARFAH (Primary Author)
Institution: Karadeniz Technical University
Country: Indonesia


Dates

Publication Date : March 30, 2021

Bibtex @research article { jnt837011, journal = {Journal of New Theory}, issn = {}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2021}, volume = {}, pages = {37 - 44}, doi = {}, title = {On Evolutes of Null Cartan Curves in Minkowski 4-Space}, key = {cite}, author = {Arfah, Arfah} }
APA Arfah, A . (2021). On Evolutes of Null Cartan Curves in Minkowski 4-Space . Journal of New Theory , (34) , 37-44 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/61070/837011
MLA Arfah, A . "On Evolutes of Null Cartan Curves in Minkowski 4-Space" . Journal of New Theory (2021 ): 37-44 <https://dergipark.org.tr/en/pub/jnt/issue/61070/837011>
Chicago Arfah, A . "On Evolutes of Null Cartan Curves in Minkowski 4-Space". Journal of New Theory (2021 ): 37-44
RIS TY - JOUR T1 - On Evolutes of Null Cartan Curves in Minkowski 4-Space AU - Arfah Arfah Y1 - 2021 PY - 2021 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 37 EP - 44 VL - IS - 34 SN - -2149-1402 M3 - UR - Y2 - 2021 ER -
EndNote %0 Journal of New Theory On Evolutes of Null Cartan Curves in Minkowski 4-Space %A Arfah Arfah %T On Evolutes of Null Cartan Curves in Minkowski 4-Space %D 2021 %J Journal of New Theory %P -2149-1402 %V %N 34 %R %U
ISNAD Arfah, Arfah . "On Evolutes of Null Cartan Curves in Minkowski 4-Space". Journal of New Theory / 34 (March 2021): 37-44 .
AMA Arfah A . On Evolutes of Null Cartan Curves in Minkowski 4-Space. JNT. 2021; (34): 37-44.
Vancouver Arfah A . On Evolutes of Null Cartan Curves in Minkowski 4-Space. Journal of New Theory. 2021; (34): 37-44.
IEEE A. Arfah , "On Evolutes of Null Cartan Curves in Minkowski 4-Space", Journal of New Theory, no. 34, pp. 37-44, Mar. 2021