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Some Characterizations of Curves in n-dimensional Euclidean Space

Yıl 2020, Cilt: 10 Sayı: 2, 1273 - 1285, 01.06.2020
https://doi.org/10.21597/jist.631448

Öz

In this work, we deal with a curve whose position vector can be expressed with the help  of Frenet Frame in  n dimensional Euclidean space n IE . We classify this type of curve with regards to curvature functions and get certain consequences for T constant,  N constant and constant ratio curves in n IE .

Kaynakça

  • Büyükkütük S, Öztürk G, 2015. Constant ratio curves according to Bishop frame in Euclidean space . General Mathematics Notes, 28: 81-91.
  • Büyükkütük S, Kişi İ, Öztürk G, 2017. A characterization of curves according to paralel transport frame in Euclidean space . New Trends in Mathematical Sciences, 5: 61-68.
  • Büyükkütük S, Kişi İ, Mishra V. N, Öztürk G. 2016. Some characterizations of curves in Galilean space . Facta Universitatis-Series Mathematics and Informatics, 31: 503-512..
  • Chen BY, 2001. Constant ratio Hypersurfaces. Soochow Journal of Mathematics, 28: 353-362.
  • Chen BY, 2003. When does the position vector of a space curve always lies in its rectifying plane? The American Mathematical Monthly, 110: 147-152.
  • Chen BY, 2002. Geometry of warped products as Riemannian submanifolds and related problems. Soochow Journal of Mathematics, 28: 125-156.
  • Chen BY, 2003. More on convolution of Riemannian manifolds. Beitrage Zur Algebra Und Geometrie, 44: 9-27.
  • Chen BY, Dillen F, 2005. Rectifying curves as centrodes and extremal curves. Bulletin of theInsituteMathematics. Acedemia Sinica, 33: 77–90.
  • Cambie S, Geomans W, Bussche IVD, 2016. Rectifying curves in the dimensional Euclidean space.Turkish Journalof Mathematics, 40: 210-223.
  • Gluck H, 1966. Higher curvatures of curvesin Euclidean space. The American Mathematical Monthly,73: 699–704.
  • Gray A, 1993. Modern differential geometry of curves and surfaces. CRS Press, Inc.
  • Gürpınar S, Arslan K, Öztürk G, 2015. A characterization of constant ratio curves in Euclidean space . Acta Universtatis Apulensis, 44: 39-51.
  • İlarslan K, Nesovic E, 2008. Some characterizations of rectifying curves in the Euclidean space . Turkish Journal of Mathematics, 32: 21-30.
  • Kişi İ, Öztürk G, 2015. Constant ratio curves according to Bishop frame in Minkowski space . Facta Universtatis, Series: Mathematics and Informatics, 30: 527-538.
  • Kişi İ, Büyükkütük S, Öztürk G, 2018. Constant ratio timelike curves in pseudo-Galilean space . Creat. Math. Inform., 27: 57-62.
  • Kişi İ, Büyükkütük S, Öztürk G, Zor A, 2017. A new characterization of curves on dual unit sphere. Journal of Abstract and Computational Mathematics, 2: 71-76.
  • Klein F, Lie S, 1871. Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendich vielen vartauschbaren Transformationen in sich ubergeben. Mathematische Annalen, 4: 50–84.
  • Öztürk G, Arslan K, Kişi İ, 2018. Constant ratio curves in Minkowski space . Matematicki Bilten, 42: 49-60.
  • Öztürk G, Büyükkütük S, Kişi İ, 2017. A characterization of curves in Galilean space . Bulletin of the Irannian Mathematical Society, 43: 771-780.
  • Öztürk G, Kişi İ, Büyükkütük S, 2017. Constant ratio quaternionic curves in Euclidean spaces. Applied Clifford Algebras, 27: 1659-1673.

Some Characterizations of Curves in n-dimensional Euclidean Space

Yıl 2020, Cilt: 10 Sayı: 2, 1273 - 1285, 01.06.2020
https://doi.org/10.21597/jist.631448

Öz

In this work, we deal with a curve whose position vector can be expressed with the help of Frenet Frame in  n dimensional Euclidean space n IE . We classify this type of curve with regards to curvature functions and get certain consequences for T constant,  N constant and constant ratio curves in n IE .

Kaynakça

  • Büyükkütük S, Öztürk G, 2015. Constant ratio curves according to Bishop frame in Euclidean space . General Mathematics Notes, 28: 81-91.
  • Büyükkütük S, Kişi İ, Öztürk G, 2017. A characterization of curves according to paralel transport frame in Euclidean space . New Trends in Mathematical Sciences, 5: 61-68.
  • Büyükkütük S, Kişi İ, Mishra V. N, Öztürk G. 2016. Some characterizations of curves in Galilean space . Facta Universitatis-Series Mathematics and Informatics, 31: 503-512..
  • Chen BY, 2001. Constant ratio Hypersurfaces. Soochow Journal of Mathematics, 28: 353-362.
  • Chen BY, 2003. When does the position vector of a space curve always lies in its rectifying plane? The American Mathematical Monthly, 110: 147-152.
  • Chen BY, 2002. Geometry of warped products as Riemannian submanifolds and related problems. Soochow Journal of Mathematics, 28: 125-156.
  • Chen BY, 2003. More on convolution of Riemannian manifolds. Beitrage Zur Algebra Und Geometrie, 44: 9-27.
  • Chen BY, Dillen F, 2005. Rectifying curves as centrodes and extremal curves. Bulletin of theInsituteMathematics. Acedemia Sinica, 33: 77–90.
  • Cambie S, Geomans W, Bussche IVD, 2016. Rectifying curves in the dimensional Euclidean space.Turkish Journalof Mathematics, 40: 210-223.
  • Gluck H, 1966. Higher curvatures of curvesin Euclidean space. The American Mathematical Monthly,73: 699–704.
  • Gray A, 1993. Modern differential geometry of curves and surfaces. CRS Press, Inc.
  • Gürpınar S, Arslan K, Öztürk G, 2015. A characterization of constant ratio curves in Euclidean space . Acta Universtatis Apulensis, 44: 39-51.
  • İlarslan K, Nesovic E, 2008. Some characterizations of rectifying curves in the Euclidean space . Turkish Journal of Mathematics, 32: 21-30.
  • Kişi İ, Öztürk G, 2015. Constant ratio curves according to Bishop frame in Minkowski space . Facta Universtatis, Series: Mathematics and Informatics, 30: 527-538.
  • Kişi İ, Büyükkütük S, Öztürk G, 2018. Constant ratio timelike curves in pseudo-Galilean space . Creat. Math. Inform., 27: 57-62.
  • Kişi İ, Büyükkütük S, Öztürk G, Zor A, 2017. A new characterization of curves on dual unit sphere. Journal of Abstract and Computational Mathematics, 2: 71-76.
  • Klein F, Lie S, 1871. Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendich vielen vartauschbaren Transformationen in sich ubergeben. Mathematische Annalen, 4: 50–84.
  • Öztürk G, Arslan K, Kişi İ, 2018. Constant ratio curves in Minkowski space . Matematicki Bilten, 42: 49-60.
  • Öztürk G, Büyükkütük S, Kişi İ, 2017. A characterization of curves in Galilean space . Bulletin of the Irannian Mathematical Society, 43: 771-780.
  • Öztürk G, Kişi İ, Büyükkütük S, 2017. Constant ratio quaternionic curves in Euclidean spaces. Applied Clifford Algebras, 27: 1659-1673.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik / Mathematics
Yazarlar

Sezgin Büyükkütük 0000-0002-1845-0822

İlim Kişi 0000-0002-4785-8165

Günay Öztürk 0000-0002-1608-0354

Kadri Arslan 0000-0002-1440-7050

Yayımlanma Tarihi 1 Haziran 2020
Gönderilme Tarihi 9 Ekim 2019
Kabul Tarihi 12 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 2

Kaynak Göster

APA Büyükkütük, S., Kişi, İ., Öztürk, G., Arslan, K. (2020). Some Characterizations of Curves in n-dimensional Euclidean Space. Journal of the Institute of Science and Technology, 10(2), 1273-1285. https://doi.org/10.21597/jist.631448
AMA Büyükkütük S, Kişi İ, Öztürk G, Arslan K. Some Characterizations of Curves in n-dimensional Euclidean Space. Iğdır Üniv. Fen Bil Enst. Der. Haziran 2020;10(2):1273-1285. doi:10.21597/jist.631448
Chicago Büyükkütük, Sezgin, İlim Kişi, Günay Öztürk, ve Kadri Arslan. “Some Characterizations of Curves in N-Dimensional Euclidean Space”. Journal of the Institute of Science and Technology 10, sy. 2 (Haziran 2020): 1273-85. https://doi.org/10.21597/jist.631448.
EndNote Büyükkütük S, Kişi İ, Öztürk G, Arslan K (01 Haziran 2020) Some Characterizations of Curves in n-dimensional Euclidean Space. Journal of the Institute of Science and Technology 10 2 1273–1285.
IEEE S. Büyükkütük, İ. Kişi, G. Öztürk, ve K. Arslan, “Some Characterizations of Curves in n-dimensional Euclidean Space”, Iğdır Üniv. Fen Bil Enst. Der., c. 10, sy. 2, ss. 1273–1285, 2020, doi: 10.21597/jist.631448.
ISNAD Büyükkütük, Sezgin vd. “Some Characterizations of Curves in N-Dimensional Euclidean Space”. Journal of the Institute of Science and Technology 10/2 (Haziran 2020), 1273-1285. https://doi.org/10.21597/jist.631448.
JAMA Büyükkütük S, Kişi İ, Öztürk G, Arslan K. Some Characterizations of Curves in n-dimensional Euclidean Space. Iğdır Üniv. Fen Bil Enst. Der. 2020;10:1273–1285.
MLA Büyükkütük, Sezgin vd. “Some Characterizations of Curves in N-Dimensional Euclidean Space”. Journal of the Institute of Science and Technology, c. 10, sy. 2, 2020, ss. 1273-85, doi:10.21597/jist.631448.
Vancouver Büyükkütük S, Kişi İ, Öztürk G, Arslan K. Some Characterizations of Curves in n-dimensional Euclidean Space. Iğdır Üniv. Fen Bil Enst. Der. 2020;10(2):1273-85.