The Directional Curves of Spacelike and Timelike Frenet Curves in 𝑬𝟏

Semra Yurttançıkmaz; Sezai Kızıltuğ; Ali Çakmak

The Directional Curves of Spacelike and Timelike Frenet Curves in 𝑬𝟏

Year 2019, Volume: 2 Issue: 3, 1 - 12, 01.10.2019

Semra Yurttançıkmaz , Sezai Kızıltuğ Ali Çakmak

Abstract

In this paper, we define some special curves by using spacelike and timelike curves in three dimensional Minkowski space. Also, we give some new characterizations and results for these curves

Keywords

Associated curves, osculating directional curves, osculating donor curves

References

B. O’Neill, Semi-Riemannian Geometry with Application to Relativity, Academic Press, New York, 1983.
T.A. Cook, The Curves of Life, Constable, London, 1914, Reprinted (Dover, London, ).
A.T. Ali, Position vectors of spacelike helices from intrinisic equations in Minkowski 3- space, Nonlinear Anal. TMA 73 (2010) 1118–1126.
L. Kula, N. Ekmekci, Y. Yayli, K. İlarslan, Characterizations of slant helices in Euclidean space, Turkish J. Math. 34 (2010) 261–274.
A. Jain, G. Wang, K.M. Vasquez, DNA triple helices: biological consequences and therapeutic potential, Biochemie 90 (2008) 1117–1130.
J.D. Watson, F.H. Crick, Molecular structures of nucleic acids, Nature 171 (1953) 737–738.
K. İlarslan, Ö. Boyacıoğlu, Position vectors of a spacelike W-curve in Minkowski Space , Bull. Korean Math. Soc. 44 (2007) 429–438.
K. İlarslan, Ö. Boyacıoğlu, Position vectors of a timelike and a null helix in Minkowski 3- space, Chaos Solitons Fractals 38 (2008) 1383–1389.
M.S. El Naschie, Experimental and theoretical arguments for the number and mass of the Higgs particles, Chaos Solitons Fractals 23 (2005) 1901–1908.
A. Çakmak, New Type Direction Curves in 3-Dimensional Compact Lie Group. Symmetry (3) (2019) 387.
B. Y. Chen, When does the position vector of a space curve always lie in its normal plane?, Amer Math. Monthly 110 (2003) 147–152.
J. H. Choi, Y. H. Kim, A. T. Ali, Some associated curves of Frenet non-lightlike curves in (2012) 394 712-723.
W. Kühnel, Differential geometry Curves-Surfaces-Manifolds, American Mathematical Society, 380, USA, 2006.
A. T. Ali, R. Lopez, Slant helices in Minkowski space , J. Korean Math. Soc. 48 (2011) , J. Korean Math. Soc. 48 (2011) –167.
J. H. Choi, Y. H. Kim, Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation 218 (2012) 9116–9124.
M. Önder, S. Kızıltuğ, Osculating direction curves and their applications, Preprint 2015: https://arxiv.org/abs/1503.07385.

Year 2019, Volume: 2 Issue: 3, 1 - 12, 01.10.2019

Semra Yurttançıkmaz , Sezai Kızıltuğ Ali Çakmak

Abstract

References

B. O’Neill, Semi-Riemannian Geometry with Application to Relativity, Academic Press, New York, 1983.
T.A. Cook, The Curves of Life, Constable, London, 1914, Reprinted (Dover, London, ).
A.T. Ali, Position vectors of spacelike helices from intrinisic equations in Minkowski 3- space, Nonlinear Anal. TMA 73 (2010) 1118–1126.
L. Kula, N. Ekmekci, Y. Yayli, K. İlarslan, Characterizations of slant helices in Euclidean space, Turkish J. Math. 34 (2010) 261–274.
A. Jain, G. Wang, K.M. Vasquez, DNA triple helices: biological consequences and therapeutic potential, Biochemie 90 (2008) 1117–1130.
J.D. Watson, F.H. Crick, Molecular structures of nucleic acids, Nature 171 (1953) 737–738.
K. İlarslan, Ö. Boyacıoğlu, Position vectors of a spacelike W-curve in Minkowski Space , Bull. Korean Math. Soc. 44 (2007) 429–438.
K. İlarslan, Ö. Boyacıoğlu, Position vectors of a timelike and a null helix in Minkowski 3- space, Chaos Solitons Fractals 38 (2008) 1383–1389.
M.S. El Naschie, Experimental and theoretical arguments for the number and mass of the Higgs particles, Chaos Solitons Fractals 23 (2005) 1901–1908.
A. Çakmak, New Type Direction Curves in 3-Dimensional Compact Lie Group. Symmetry (3) (2019) 387.
B. Y. Chen, When does the position vector of a space curve always lie in its normal plane?, Amer Math. Monthly 110 (2003) 147–152.
J. H. Choi, Y. H. Kim, A. T. Ali, Some associated curves of Frenet non-lightlike curves in (2012) 394 712-723.
W. Kühnel, Differential geometry Curves-Surfaces-Manifolds, American Mathematical Society, 380, USA, 2006.
A. T. Ali, R. Lopez, Slant helices in Minkowski space , J. Korean Math. Soc. 48 (2011) , J. Korean Math. Soc. 48 (2011) –167.
J. H. Choi, Y. H. Kim, Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation 218 (2012) 9116–9124.
M. Önder, S. Kızıltuğ, Osculating direction curves and their applications, Preprint 2015: https://arxiv.org/abs/1503.07385.

There are 16 citations in total.

Details

Primary Language	English
Journal Section	Some Notes on the Extendibility of an Especial Family of Diophantine 𝑷𝟐 Pairs
Authors	Semra Yurttançıkmaz Sezai Kızıltuğ This is me Ali Çakmak This is me
Publication Date	October 1, 2019
Published in Issue	Year 2019 Volume: 2 Issue: 3

Cite

APA	Yurttançıkmaz, S., Kızıltuğ, S., & Çakmak, A. (2019). The Directional Curves of Spacelike and Timelike Frenet Curves in 𝑬𝟏. Journal of Advanced Mathematics and Mathematics Education, 2(3), 1-12.