Special Curves According to Extended Darboux Frame Field in 𝔼𝟏 𝟒

Year 2021, Volume: 16 Issue: 2, 221 - 230, 15.09.2021

Esra Erdem , Mihriban Alyamac Kulahci , Münevver Yıldırım Yılmaz

Abstract

In this study, the involute of a curve is investigated in Minkowski space-time by using extended Darboux frame field
and curves of the AW (k) type are studied in Minkowski space-time.

Keywords

Involute curve, Minkowski Space-Time, Extended Darboux Frame Field

References

• Referans1 Dirişen B.C, Şahin T. Position Vectors of With Respect to Darboux Frame In The Galilean Space . arXiv:1707. 03930v2.(2017).
• Referans2 Altunkaya B, Aksoyak F. K. Curves of Constant Breadth According To Darboux Frame, Commun. Fac. Sci. Univ. Ank. Series A1. (2017); 66(2):44-52.
• Referans3 Düldül M, Düldül B, Kuruoğlu N, Özdamar E. Extension of the Darboux frame into Euclidean 4-space and its invariants. Turkish Journal of Mathematics. (2017); 41: 1628-1639.
• Referans4 Boyer C. A History of Mathematics New York: Wiley. (1968).
• Referans 5 Turgut M,Yilmaz S. On The Frenet Frame and A Characterization of space-like Involute-Evolute Curve Couple in Minkowski Space-time. Int. Math. Forum. (2008); 3(16): 793-801.
• Referans6 Soyfidan T, Güngör M. A. On the Quaternionic involute-evolute curves. arXiv: 1311.0621.[math. GT]. (2013).
• Referans7 As E, Sarıoğlugil A. On the Bishop curvatures of involute-evolute curve couple in 𝔼3. Internatonal Journal of Physical Sciences.(2014); 9(7):140-145 .
• Referans8 Külahcı M, Bektaş M, Ergüt M. Curves of AW (k) -type in 3-dimensional nul cone. Phys. Lett. A. (2007); 371:275-277.
• Referans9 Sun J, Pei D. Null Cartan Bertrand curves of AW (k) -type in Minkowski 4-space. School of Mathematics and Statistics. Northeast Normal University. Changchun, 130024, PR China. (2012).
• Referans10 Arslan K, Çelik Y, Deszcz R, Özgür C. Submanifolds all of whose normal sections are W-curves. Far East J. Math. Sci. (1997); 5(4): 537-544.
• Referans11 Yoon D.W. General Helices of AW(k) -Type in the Lie Group J. Appl. Math. (2012).
• Referans12 Arslan K, Özgür C. Curves and Surfaces of AW (k) Type. Geometry and Topology of Submanifolds IX. World Scientific. (1997); 21-26.
• Referans13 Özgür C, Gezgin F. On some curves of AW(k)-type. Differential Geometry-Dynamical Systems. (2005); 7:74-80.
• Referans14 Kılıç B,Arslan K. On Curves and Surfaces of AW(k)-type. BAÜ Fen Bil. Enst. Dergisi. (2004); 6(1):52-61.
• Referans15 O'Neill B. Semi Riemannian Geometry. Academic Press. New York-London.(1983).
• Referans 16 İlarslan K, Nesovic E. Spacelike and timelike normal curves in Minkowski space time. Publications de L'institut Mathematique, Nouvelle serie. (2009); 85:111-118.
• Referans17 Düldül B. Extended Darboux frame field in Minkowsk space-time 𝔼14. Malaya Journal of Matematik. (2018); 6(3): 473-477.