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DOI:http://dx.doi.org/10.26855/jamc.2021.03.007

Rotation Minimizing Frame and Rectifying Curves in E_1^n

Date: March 17,2021 |Hits: 395 Download PDF How to cite this paper

Özgür Keskin*, Yusuf Yayli

Faculty of Science, Department of Mathematics, Ankara University, Ankara, Turkey.

*Corresponding author: Özgür Keskin

Abstract

In this paper, some applications of a Rotation minimizing frame (RMF) are studied in E_1^4 and in E_1^n for timelike, spacelike curves. Firstly, in E_1^4, a Rotation minimizing frame (RMF) is obtained on the timelike and spacelike direction curves ∫ N(s) ds. The features of this Rotation minimizing frame are expressed. Secondly, it is determined when the timelike and spacelike curves can be rectifying curves. In addition, it has been investigated the conditions under which timelike and spacelike curves can be sphere calcurves. Then, a new characterization of rectifying curves is given, similar to the characterization of spherical curves. Finally, this Rotation minimizing frame is generalized in E_1^n for timelike, spacelike curves. In E_1^n, the conditions being a spherical curve and arectifying curve are given thank to this frame for timelike and spacelike curves. Also, a relationship between the spherical curve and the rectifying curve is stated. It is shown that the coefficients used in obtaining rectifying curves are constant numbers.

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How to cite this paper

Rotation Minimizing Frame and Rectifying Curves in E_1^n

How to cite this paper: Özgür Keskin, Yusuf Yayli. (2021) Rotation Minimizing Frame and Rectifying Curves in E_1^n. Journal of Applied Mathematics and Computation5(1), 56-67.

DOI: http://dx.doi.org/10.26855/jamc.2021.03.007

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