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.
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.
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.
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.