Singularities of the Ruled Surfaces According to RM Frame and Natural Lift Curves-Reference-Cited by-同舟云学术

Singularities of the Ruled Surfaces According to RM Frame and Natural Lift Curves

Published:2022-06-29 Issue:2 Volume:43 Page:308-315
ISSN:2587-2680
Container-title:Cumhuriyet Science Journal
language:en
Short-container-title:CSJ

Author:

KARACA Emel¹

Affiliation:

1. Ankara Hacı Bayram Veli Üniversitesi

Abstract

In this study, the ruled surface generated by the natural lift curve in IR^3 is obtained by using the isomorphism between unit dual sphere, DS^2 and the subset of the tangent bundle of unit 2-sphere, T\bar{M}. Then, exploitting E. Study mapping and the isomorphism mentioned below, each natural lift curve on T\bar{M} is corresponded to the ruled surface in IR^3. Moreover, the singularities of this ruled surface are examined according to RM vectors and these ruled surfaces have been classified. Some examples are given to support the main results.

Publisher

Cumhuriyet University

Subject

General Medicine

Reference22 articles.

1. [1] Wang W., Juttler B., Zheng D., Liu Y., Computation of Rotation Minimizing Frame, ACM Trans. Graph., 27(1) (2008) 1-18.

2. [2] Bishop R.L., There is More Than One Way to Frame A Curve, Amer. Math. Monthly, 8(246) (1975) 1, 2.

3. [3] Do Carmo M.P., Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs, NJ, (1976).

4. [4] Dede M., Why Flc- Frame is Better than Frenet Frame? DOI: 10.13140/RG.2.2.23418.24002 (2019).

5. [5] Ravani R., Meghdari A., Ravani B., Rational Frenet-Serret Curves and Rotation Minimizing Frames in Spatial Motion Design, IEEE International Conference on Intelligent Engineering Systems, INES (2004) 186-192.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Another application of Smarandache based ruled surfaces with the Darboux vector according to Frenet frame in $E^{3}$;Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics;2023-07-08