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A characterization of curves according to parallel transport frame in Euclidean n-space E^n

Yıl 2017, Cilt: 5 Sayı: 2, 61 - 68, 30.03.2017

Sezgin Buyukkutuk İlim Kisi Gunay Ozturk

Öz

The position vector of a regular curve in Euclidean n-space En can be written as a linear combination of its parallel transport vectors. In the present study, we characterize such curves in terms of their curvature functions. Further, we obtain some results of constant ratio, T-constant and N-constant type curves in En.

Anahtar Kelimeler

Parallel transport frame position vector

Kaynakça

  • L. R. Bishop, There is more than one way to frame a curve, Amer. Math. Monthly 82(3)(1975) 246-251.
  • S. Buyukkutuk, G. Ozturk, Constant ratio curves according to Bishop frame in Euclidean 3-space E3, Gen. Math. Notes 28(1)(2015) 81-91.
  • S. Buyukkutuk, G. Ozturk, Constant ratio curves according to parallel transport frame in Euclidean 4-space E4, New Trends in Mathematical Sciences 4(3) (2015) 171-178.
  • B.Y. Chen, Constant ratio hypersurfaces, Soochow J. Math. 28 (2001) 353-362.
  • B.Y. Chen, When does the position vector of a space curve always lies in its rectifying plane?, Amer. Math. Monthly 110 (2003) 147-152.
  • B.Y. Chen, Geometry of Warped Products as Riemannian Submanifolds and Related Problemsc, Soochow Journal ofMathematics, 28(2) (2002) 125-156.
  • B.Y. Chen, More on convolution of Riemannian manifolds, Beitrage Algebra und Geom. 44 (2003) 9-24.
  • S. Cambie,W. Geomans, I.V.D Bussche, Rectifying curves in the n-dimensional Euclidean space, Turk J.Math 40 (2016) 210-223.
  • H. Gluck, Higher curvatures of curves in Euclidean space, The American Mathematical Monthly 73(7) (1966) 699-704.
  • S. Gurpınar, K. Arslan, G. Ozturk, A characterization of constant-ratio curves in Euclidean 3-space E3, Acta Universitatis Apulensis 44 (2015) 39-51.
  • K. Ilarslan and E. Nesovic, Some characterizations of rectifying curves in the Euclidean space E4, Turk. J. Math. 32 (2008) 21-30.
  • I. Kisi, G. Ozturk, Constant ratio curves according to Bishop frame in Minkowski 3-space E31 , Facta Universitatis, Series: Mathematics and Informatics 30(4) (2015) 527-538.
  • C.L. Terng, Lecture notes on curves and surfaces in R3, Preliminary Version and in Progress, April 2, 2003.

Yıl 2017, Cilt: 5 Sayı: 2, 61 - 68, 30.03.2017

Sezgin Buyukkutuk İlim Kisi Gunay Ozturk

Öz

Kaynakça

  • L. R. Bishop, There is more than one way to frame a curve, Amer. Math. Monthly 82(3)(1975) 246-251.
  • S. Buyukkutuk, G. Ozturk, Constant ratio curves according to Bishop frame in Euclidean 3-space E3, Gen. Math. Notes 28(1)(2015) 81-91.
  • S. Buyukkutuk, G. Ozturk, Constant ratio curves according to parallel transport frame in Euclidean 4-space E4, New Trends in Mathematical Sciences 4(3) (2015) 171-178.
  • B.Y. Chen, Constant ratio hypersurfaces, Soochow J. Math. 28 (2001) 353-362.
  • B.Y. Chen, When does the position vector of a space curve always lies in its rectifying plane?, Amer. Math. Monthly 110 (2003) 147-152.
  • B.Y. Chen, Geometry of Warped Products as Riemannian Submanifolds and Related Problemsc, Soochow Journal ofMathematics, 28(2) (2002) 125-156.
  • B.Y. Chen, More on convolution of Riemannian manifolds, Beitrage Algebra und Geom. 44 (2003) 9-24.
  • S. Cambie,W. Geomans, I.V.D Bussche, Rectifying curves in the n-dimensional Euclidean space, Turk J.Math 40 (2016) 210-223.
  • H. Gluck, Higher curvatures of curves in Euclidean space, The American Mathematical Monthly 73(7) (1966) 699-704.
  • S. Gurpınar, K. Arslan, G. Ozturk, A characterization of constant-ratio curves in Euclidean 3-space E3, Acta Universitatis Apulensis 44 (2015) 39-51.
  • K. Ilarslan and E. Nesovic, Some characterizations of rectifying curves in the Euclidean space E4, Turk. J. Math. 32 (2008) 21-30.
  • I. Kisi, G. Ozturk, Constant ratio curves according to Bishop frame in Minkowski 3-space E31 , Facta Universitatis, Series: Mathematics and Informatics 30(4) (2015) 527-538.
  • C.L. Terng, Lecture notes on curves and surfaces in R3, Preliminary Version and in Progress, April 2, 2003.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Sezgin Buyukkutuk

İlim Kisi Bu kişi benim

Gunay Ozturk Bu kişi benim

Yayımlanma Tarihi 30 Mart 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 2

Kaynak Göster

APA Buyukkutuk, S., Kisi, İ., & Ozturk, G. (2017). A characterization of curves according to parallel transport frame in Euclidean n-space E^n. New Trends in Mathematical Sciences, 5(2), 61-68.
AMA Buyukkutuk S, Kisi İ, Ozturk G. A characterization of curves according to parallel transport frame in Euclidean n-space E^n. New Trends in Mathematical Sciences. Mart 2017;5(2):61-68.
Chicago Buyukkutuk, Sezgin, İlim Kisi, ve Gunay Ozturk. “A Characterization of Curves According to Parallel Transport Frame in Euclidean N-Space E^n”. New Trends in Mathematical Sciences 5, sy. 2 (Mart 2017): 61-68.
EndNote Buyukkutuk S, Kisi İ, Ozturk G (01 Mart 2017) A characterization of curves according to parallel transport frame in Euclidean n-space E^n. New Trends in Mathematical Sciences 5 2 61–68.
IEEE S. Buyukkutuk, İ. Kisi, ve G. Ozturk, “A characterization of curves according to parallel transport frame in Euclidean n-space E^n”, New Trends in Mathematical Sciences, c. 5, sy. 2, ss. 61–68, 2017.
ISNAD Buyukkutuk, Sezgin vd. “A Characterization of Curves According to Parallel Transport Frame in Euclidean N-Space E^n”. New Trends in Mathematical Sciences 5/2 (Mart 2017), 61-68.
JAMA Buyukkutuk S, Kisi İ, Ozturk G. A characterization of curves according to parallel transport frame in Euclidean n-space E^n. New Trends in Mathematical Sciences. 2017;5:61–68.
MLA Buyukkutuk, Sezgin vd. “A Characterization of Curves According to Parallel Transport Frame in Euclidean N-Space E^n”. New Trends in Mathematical Sciences, c. 5, sy. 2, 2017, ss. 61-68.
Vancouver Buyukkutuk S, Kisi İ, Ozturk G. A characterization of curves according to parallel transport frame in Euclidean n-space E^n. New Trends in Mathematical Sciences. 2017;5(2):61-8.
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