Some Characterizations of Curves in n-dimensional Euclidean Space

Year 2020, , 1273 - 1285, 01.06.2020

Sezgin Büyükkütük , İlim Kişi , Günay Öztürk , Kadri Arslan

https://doi.org/10.21597/jist.631448

Cited By: 1

Abstract

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 .

Keywords

Constant ratio curves, position vector, W curves

Some Characterizations of Curves in n-dimensional Euclidean Space

Abstract

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 .

Keywords

Constant ratio curves, W-curves, position vector

References

• 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.