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

Year 2017, Volume: 5 Issue: 2, 61 - 68, 30.03.2017

Sezgin Buyukkutuk , İlim Kisi Gunay Ozturk

Abstract

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.

Keywords

Parallel transport frame position vector

References

  • 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.

Year 2017, Volume: 5 Issue: 2, 61 - 68, 30.03.2017

Sezgin Buyukkutuk , İlim Kisi Gunay Ozturk

Abstract

References

  • 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.
There are 13 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Sezgin Buyukkutuk

İlim Kisi This is me

Gunay Ozturk This is me

Publication Date March 30, 2017
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

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. March 2017;5(2):61-68.
Chicago Buyukkutuk, Sezgin, İlim Kisi, and Gunay Ozturk. “A Characterization of Curves According to Parallel Transport Frame in Euclidean N-Space E^n”. New Trends in Mathematical Sciences 5, no. 2 (March 2017): 61-68.
EndNote Buyukkutuk S, Kisi İ, Ozturk G (March 1, 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, and G. Ozturk, “A characterization of curves according to parallel transport frame in Euclidean n-space E^n”, New Trends in Mathematical Sciences, vol. 5, no. 2, pp. 61–68, 2017.
ISNAD Buyukkutuk, Sezgin et al. “A Characterization of Curves According to Parallel Transport Frame in Euclidean N-Space E^n”. New Trends in Mathematical Sciences 5/2 (March 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 et al. “A Characterization of Curves According to Parallel Transport Frame in Euclidean N-Space E^n”. New Trends in Mathematical Sciences, vol. 5, no. 2, 2017, pp. 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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