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

Yıl 2016, Cilt: 16 Sayı: 3, 569 - 575, 31.12.2016

Günay Öztürk

Öz

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 .

Anahtar Kelimeler

İnvolüt Space-like Eğri W-eğrisi; Helis.

Kaynakça

  • 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.

Yıl 2016, Cilt: 16 Sayı: 3, 569 - 575, 31.12.2016

Günay Öztürk

Öz

Kaynakça

  • 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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Günay Öztürk

Yayımlanma Tarihi 31 Aralık 2016
Gönderilme Tarihi 25 Nisan 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 16 Sayı: 3

Kaynak Göster

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. Aralık 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, sy. 3 (Aralık 2016): 569-75.
EndNote Öztürk G (01 Aralık 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, c. 16, sy. 3, ss. 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 (Aralık 2016), 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, c. 16, sy. 3, 2016, ss. 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.