Special Curves According to Extended Darboux Frame Field in 𝔼𝟏 𝟒

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

1. Referans1 Dirişen B.C, Şahin T. Position Vectors of With Respect to Darboux Frame In The Galilean Space . arXiv:1707. 03930v2.(2017).
2. 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.
3. 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.
4. Referans4 Boyer C. A History of Mathematics New York: Wiley. (1968).
5. 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.
6. Referans6 Soyfidan T, Güngör M. A. On the Quaternionic involute-evolute curves. arXiv: 1311.0621.[math. GT]. (2013).
7. 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 .
8. Referans8 Külahcı M, Bektaş M, Ergüt M. Curves of AW (k) -type in 3-dimensional nul cone. Phys. Lett. A. (2007); 371:275-277.

9. 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).
10. 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.
11. Referans11 Yoon D.W. General Helices of AW(k) -Type in the Lie Group J. Appl. Math. (2012).
12. Referans12 Arslan K, Özgür C. Curves and Surfaces of AW (k) Type. Geometry and Topology of Submanifolds IX. World Scientific. (1997); 21-26.
13. Referans13 Özgür C, Gezgin F. On some curves of AW(k)-type. Differential Geometry-Dynamical Systems. (2005); 7:74-80.
14. Referans14 Kılıç B,Arslan K. On Curves and Surfaces of AW(k)-type. BAÜ Fen Bil. Enst. Dergisi. (2004); 6(1):52-61.
15. Referans15 O'Neill B. Semi Riemannian Geometry. Academic Press. New York-London.(1983).
16. 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.
17. Referans17 Düldül B. Extended Darboux frame field in Minkowsk space-time 𝔼14. Malaya Journal of Matematik. (2018); 6(3): 473-477.