EN
A characterization of curves according to parallel transport frame in Euclidean n-space E^n
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
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.
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Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Publication Date
March 30, 2017
Submission Date
May 17, 2016
Acceptance Date
June 17, 2016
Published in Issue
Year 2017 Volume: 5 Number: 2
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. https://izlik.org/JA96CZ54YY
AMA
1.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):61-68. https://izlik.org/JA96CZ54YY
Chicago
Buyukkutuk, Sezgin, İlim Kisi, and Gunay Ozturk. 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. https://izlik.org/JA96CZ54YY.
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
[1]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, Mar. 2017, [Online]. Available: https://izlik.org/JA96CZ54YY
ISNAD
Buyukkutuk, Sezgin - Kisi, İlim - Ozturk, Gunay. “A Characterization of Curves According to Parallel Transport Frame in Euclidean N-Space E^n”. New Trends in Mathematical Sciences 5/2 (March 1, 2017): 61-68. https://izlik.org/JA96CZ54YY.
JAMA
1.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, Mar. 2017, pp. 61-68, https://izlik.org/JA96CZ54YY.
Vancouver
1.Sezgin Buyukkutuk, İlim Kisi, Gunay Ozturk. A characterization of curves according to parallel transport frame in Euclidean n-space E^n. New Trends in Mathematical Sciences [Internet]. 2017 Mar. 1;5(2):61-8. Available from: https://izlik.org/JA96CZ54YY