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On Involutes of Order k of a Space-like Curve in Minkowski 4-space 4 1

Year 2016, Volume: 16 Issue: 3, 569 - 575, 31.12.2016

Günay Öztürk

Abstract

The orthogonal trajectories of the first tangents of a curve x are called the involutes of x. In this study,
we give a characterization of involutes of order k of a space-like curve x with time-like principal normal
in Minkowski 4-space 4
1 IE .

Keywords

İnvolüt Space-like Eğri W-eğrisi; Helis.

References

  • Blazenka, D. And Zeljka M.S.,1999. Involutes and evolutes in n-dimensional simply isotropic space. Journal of Information and Organizational Sciences, 2(3), 71-79.
  • Gluck, H., 1966. Higher curvatures of curves in Euclidean space. American Mathematical Monthly, 73, 699-704.
  • Kılıc, B., Arslan, K. and Öztürk, G., 2008. Tangentially cubic curves in Euclidean spaces. Differential Geometry- Dynamical Systems, 10, 186-196.
  • Klein, F. and Lie, S., 1871. Uber diejenigen ebenenen kurven welche durch eingeschlossenes system von einfach unendlich vielen vartauschbaren linearen transformationen in sich übergehen. Mathematische Annalen, 4, 50-84.
  • Monterde, J., 2007. Curves with constant curvature ratios. Bulletin of Mexican Mathematic Society, Ser. 3A, 13(1), 177-186.
  • O'Neill, B., 1983. Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York. Öztürk, G., Arslan, K. and Hacisalihoglu, H. H., 2008. A characterization of ccr-curves in m IR . Proccedings of Estonian Academy Science, 57(4), 217-224.
  • Öztürk, G., Arslan, K. and Bulca, B., 2016. A characterization of involutes and evolutes of a given curve in n IE . arxiv.org.
  • Salkowski E., 1909. Zur transformation von raumkurven. Mathematische Annalen, 66(4), 517-557.
  • Turgut, M., Ali, A.T., and Lopez-Bonilla, J. L., 2010. Timelike involutes of a space-like helix in Minkowski spacetime. Apeiron, 17(1), 28-41.
  • Walfare, J., 1995. Curves and surfaces in Minkowski space. PhD thesis, K.U. Leuven, Faculty of Science, Leuven.
  • Yılmaz, S. and Turgut, M., 2008. On the differential geometry of the curves in Minkowski space-time I. International Journal of Contemporary Mathematical Science, 3(27), 1343-1349.

Year 2016, Volume: 16 Issue: 3, 569 - 575, 31.12.2016

Günay Öztürk

Abstract

References

  • Blazenka, D. And Zeljka M.S.,1999. Involutes and evolutes in n-dimensional simply isotropic space. Journal of Information and Organizational Sciences, 2(3), 71-79.
  • Gluck, H., 1966. Higher curvatures of curves in Euclidean space. American Mathematical Monthly, 73, 699-704.
  • Kılıc, B., Arslan, K. and Öztürk, G., 2008. Tangentially cubic curves in Euclidean spaces. Differential Geometry- Dynamical Systems, 10, 186-196.
  • Klein, F. and Lie, S., 1871. Uber diejenigen ebenenen kurven welche durch eingeschlossenes system von einfach unendlich vielen vartauschbaren linearen transformationen in sich übergehen. Mathematische Annalen, 4, 50-84.
  • Monterde, J., 2007. Curves with constant curvature ratios. Bulletin of Mexican Mathematic Society, Ser. 3A, 13(1), 177-186.
  • O'Neill, B., 1983. Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York. Öztürk, G., Arslan, K. and Hacisalihoglu, H. H., 2008. A characterization of ccr-curves in m IR . Proccedings of Estonian Academy Science, 57(4), 217-224.
  • Öztürk, G., Arslan, K. and Bulca, B., 2016. A characterization of involutes and evolutes of a given curve in n IE . arxiv.org.
  • Salkowski E., 1909. Zur transformation von raumkurven. Mathematische Annalen, 66(4), 517-557.
  • Turgut, M., Ali, A.T., and Lopez-Bonilla, J. L., 2010. Timelike involutes of a space-like helix in Minkowski spacetime. Apeiron, 17(1), 28-41.
  • Walfare, J., 1995. Curves and surfaces in Minkowski space. PhD thesis, K.U. Leuven, Faculty of Science, Leuven.
  • Yılmaz, S. and Turgut, M., 2008. On the differential geometry of the curves in Minkowski space-time I. International Journal of Contemporary Mathematical Science, 3(27), 1343-1349.
There are 11 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Günay Öztürk

Submission Date April 25, 2016
Publication Date December 31, 2016
Published in Issue Year 2016 Volume: 16 Issue: 3

Cite

APA Öztürk, G. (2016). On Involutes of Order k of a Space-like Curve in Minkowski 4-space 4 1. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 16(3), 569-575.
AMA Öztürk G. On Involutes of Order k of a Space-like Curve in Minkowski 4-space 4 1. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. December 2016;16(3):569-575.
Chicago Öztürk, Günay. “On Involutes of Order K of a Space-Like Curve in Minkowski 4-Space 4 1”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 16, no. 3 (December 2016): 569-75.
EndNote Öztürk G (December 1, 2016) On Involutes of Order k of a Space-like Curve in Minkowski 4-space 4 1. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 16 3 569–575.
IEEE G. Öztürk, “On Involutes of Order k of a Space-like Curve in Minkowski 4-space 4 1”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 16, no. 3, pp. 569–575, 2016.
ISNAD Öztürk, Günay. “On Involutes of Order K of a Space-Like Curve in Minkowski 4-Space 4 1”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 16/3 (December2016), 569-575.
JAMA Öztürk G. On Involutes of Order k of a Space-like Curve in Minkowski 4-space 4 1. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2016;16:569–575.
MLA Öztürk, Günay. “On Involutes of Order K of a Space-Like Curve in Minkowski 4-Space 4 1”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 16, no. 3, 2016, pp. 569-75.
Vancouver Öztürk G. On Involutes of Order k of a Space-like Curve in Minkowski 4-space 4 1. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2016;16(3):569-75.


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