A STUDY OF THE TUBULAR SURFACES ACCORDING TO MODIFIED ORTHOGONAL FRAME WITH TORSION

被引：0
|
作者：
Atalay, Gulnur Saffak [1 ]
机构：
[1] Ondokuz Mayis Univ, Fac Educ, Dept Math Sci, Samsun, Turkiye
来源：
HONAM MATHEMATICAL JOURNAL | 2024年 / 46卷 / 02期
关键词：
tubular surface; modified orthogonal frame with torsion; geo- desic curve; asymptotic curve; line of curvature; CURVES;
D O I：
10.5831/HMJ.2024.46.2.279
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this study, tubular surfaces were introduced according to the modified orthogonal frame defined at the points where the torsion is different from zero in the 3-dimensional Euclidean space. First, the relations between the Frenet frame and the modified orthogonal frame with torsion are given. Then, the singularity, Gaussian curvature, mean curvature and basic forms of the tubular surface given according to the modified orthogonal frame with torsion were calculated. In addition, the conditions for the parameter curves of the tubular surface to be geodesic, asymptotic and line of curvature were examined. Finally, tubular surface examples based on both the Frenet frame and the modified orthogonal frame with torsion were given to support the study.
引用
收藏
页码：279 / 290
页数：12
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