Research Article
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Conjugate mates for non-null Frenet curves

Year 2019, Volume: 23 Issue: 4, 600 - 604, 01.08.2019
https://doi.org/10.16984/saufenbilder.494471

Abstract

For each non-null Frenet curve \gamma in Minkowski 3-space, there exists a unique unit speed non-null curve tangent
to the principal binormal vector field of \gamma. We briefly call this curve the conjugate mate of\gamma . The aim of this
paper is to prove some relationships between a non-null Frenet curve and its non-null conjugate mate.

References

  • [1] M. P. O'Neill, Semi-Riemannian Geometry with Applications to Relativity. World Scientific, New York, 1983.
  • [2] W. Kuhnel, Differential geometry: curves surfaces-manifolds. Weisbaden: Braunschweig 1999.
  • [3] S. Desmukh, BY. Chen and A. Alghanemi , Natural mates of Frenet curves in Euclidean 3-space, Turk. J. Math, (2018) 42: 2826-2840.
  • [4] J. Choi, Y. H. Kim, Associated curves of a Frenet curve and their applications, Appl. Math. Comput, 2012; 218: 9116-9124.
  • [5] J. Choi , Y. H. Kim, Ali A.T., Some associated curves of Frenet non-lightlike curves in E31, J. Math. Anal. Appl. 394 (2012) 712723.
  • [6] S. Deshmukh , I. Al-Dayel, K. Ilarslan, Frenet curves in Euclidean 4-space, Int. Electron. J Geom 2017; 10: 56-66.
  • [7] S. Deshmukh, BY Chen , NB Turki, A differential equations for Frenet curves in Euclidean 3-space and its applications, Rom. J. Math. Comput. Sci., 2018; 8: 1.
  • [8] H. Balgetir, M. Bektaş , M. Ergut, Bertrand curves for nonnull curves in 3-dimensional Lorentzian space, Hadronic Journal 27 (2004) 229-236.
  • [9] J. H. Choi, T. H. Kang and Y. H. Kim, Bertrand curves in 3-dimensional space forms, Applied Mathematics and Computation, 219 (2012) 1040-1046. [10] K. Ilarslan, E. Nesovic , M. Petrovic-Torgasev, Some characterizations of rectifying curves in the Minkowski 3-space, Novi Sad J. Math. 33(2) (2003), 23-32.
  • [11] A. T. Ali, R. Lopez, Slant helices in Minkowski space E31, J. Korean Math. Soc. 48 (2011) 159167.
  • [12] B. Bükçü, M. K. Karacan, On the Involute and Evolute Curves of the Spacelike Curve with a Spacelike Binormal in Minkowski 3−Space , Int. J. Contemp. Math. Sciences, Vol. 2, 2007, no. 5, 221 – 232.
  • [13] B. Bükçü, M. K. Karacan, On the Involute and Evolute Curves of the Timelike Curve in Minkowski 3−Space, Demonstratio Mathematica, Vol. XL No 3 2007.
  • [14] S. K. Nurkan, I. A. Güven, M. K. Karacan, Characterizations of adjoint curves in Euclidean 3-space. Proc Natl Acad Sci. India Sect A Phys Sci. https://doi.org/10.1007/s40010-017-0425-y.
  • [15] A.T. Ali, Spacelike Salkowski and anti-Salkowski curves with spacelike principal normal in Minkowski 3-space, Int. J. Open Problems Comp. Math. 2 (2009) 451–460.
  • [16] A.T. Ali, Timelike Salkowski and anti-Salkowski curves in Minkowski 3- space, J. Adv. Res. Dyn. Cont. Syst. 2 (2010) 17–26.
  • [17] A.T. Ali, Spacelike Salkowski and anti-Salkowski curves with timelike principal normal in Minkowski 3-space, Mathematica Aeterna, Vol. 1, 2011, no. 04, 201 - 210.
Year 2019, Volume: 23 Issue: 4, 600 - 604, 01.08.2019
https://doi.org/10.16984/saufenbilder.494471

Abstract

References

  • [1] M. P. O'Neill, Semi-Riemannian Geometry with Applications to Relativity. World Scientific, New York, 1983.
  • [2] W. Kuhnel, Differential geometry: curves surfaces-manifolds. Weisbaden: Braunschweig 1999.
  • [3] S. Desmukh, BY. Chen and A. Alghanemi , Natural mates of Frenet curves in Euclidean 3-space, Turk. J. Math, (2018) 42: 2826-2840.
  • [4] J. Choi, Y. H. Kim, Associated curves of a Frenet curve and their applications, Appl. Math. Comput, 2012; 218: 9116-9124.
  • [5] J. Choi , Y. H. Kim, Ali A.T., Some associated curves of Frenet non-lightlike curves in E31, J. Math. Anal. Appl. 394 (2012) 712723.
  • [6] S. Deshmukh , I. Al-Dayel, K. Ilarslan, Frenet curves in Euclidean 4-space, Int. Electron. J Geom 2017; 10: 56-66.
  • [7] S. Deshmukh, BY Chen , NB Turki, A differential equations for Frenet curves in Euclidean 3-space and its applications, Rom. J. Math. Comput. Sci., 2018; 8: 1.
  • [8] H. Balgetir, M. Bektaş , M. Ergut, Bertrand curves for nonnull curves in 3-dimensional Lorentzian space, Hadronic Journal 27 (2004) 229-236.
  • [9] J. H. Choi, T. H. Kang and Y. H. Kim, Bertrand curves in 3-dimensional space forms, Applied Mathematics and Computation, 219 (2012) 1040-1046. [10] K. Ilarslan, E. Nesovic , M. Petrovic-Torgasev, Some characterizations of rectifying curves in the Minkowski 3-space, Novi Sad J. Math. 33(2) (2003), 23-32.
  • [11] A. T. Ali, R. Lopez, Slant helices in Minkowski space E31, J. Korean Math. Soc. 48 (2011) 159167.
  • [12] B. Bükçü, M. K. Karacan, On the Involute and Evolute Curves of the Spacelike Curve with a Spacelike Binormal in Minkowski 3−Space , Int. J. Contemp. Math. Sciences, Vol. 2, 2007, no. 5, 221 – 232.
  • [13] B. Bükçü, M. K. Karacan, On the Involute and Evolute Curves of the Timelike Curve in Minkowski 3−Space, Demonstratio Mathematica, Vol. XL No 3 2007.
  • [14] S. K. Nurkan, I. A. Güven, M. K. Karacan, Characterizations of adjoint curves in Euclidean 3-space. Proc Natl Acad Sci. India Sect A Phys Sci. https://doi.org/10.1007/s40010-017-0425-y.
  • [15] A.T. Ali, Spacelike Salkowski and anti-Salkowski curves with spacelike principal normal in Minkowski 3-space, Int. J. Open Problems Comp. Math. 2 (2009) 451–460.
  • [16] A.T. Ali, Timelike Salkowski and anti-Salkowski curves in Minkowski 3- space, J. Adv. Res. Dyn. Cont. Syst. 2 (2010) 17–26.
  • [17] A.T. Ali, Spacelike Salkowski and anti-Salkowski curves with timelike principal normal in Minkowski 3-space, Mathematica Aeterna, Vol. 1, 2011, no. 04, 201 - 210.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Alev Kelleci 0000-0003-2528-2131

Publication Date August 1, 2019
Submission Date December 10, 2018
Acceptance Date February 5, 2019
Published in Issue Year 2019 Volume: 23 Issue: 4

Cite

APA Kelleci, A. (2019). Conjugate mates for non-null Frenet curves. Sakarya University Journal of Science, 23(4), 600-604. https://doi.org/10.16984/saufenbilder.494471
AMA Kelleci A. Conjugate mates for non-null Frenet curves. SAUJS. August 2019;23(4):600-604. doi:10.16984/saufenbilder.494471
Chicago Kelleci, Alev. “Conjugate Mates for Non-Null Frenet Curves”. Sakarya University Journal of Science 23, no. 4 (August 2019): 600-604. https://doi.org/10.16984/saufenbilder.494471.
EndNote Kelleci A (August 1, 2019) Conjugate mates for non-null Frenet curves. Sakarya University Journal of Science 23 4 600–604.
IEEE A. Kelleci, “Conjugate mates for non-null Frenet curves”, SAUJS, vol. 23, no. 4, pp. 600–604, 2019, doi: 10.16984/saufenbilder.494471.
ISNAD Kelleci, Alev. “Conjugate Mates for Non-Null Frenet Curves”. Sakarya University Journal of Science 23/4 (August 2019), 600-604. https://doi.org/10.16984/saufenbilder.494471.
JAMA Kelleci A. Conjugate mates for non-null Frenet curves. SAUJS. 2019;23:600–604.
MLA Kelleci, Alev. “Conjugate Mates for Non-Null Frenet Curves”. Sakarya University Journal of Science, vol. 23, no. 4, 2019, pp. 600-4, doi:10.16984/saufenbilder.494471.
Vancouver Kelleci A. Conjugate mates for non-null Frenet curves. SAUJS. 2019;23(4):600-4.