Ruled like surfaces in three dimensional Euclidean space

被引:0
|
作者
Pal, Buddhadev [1 ]
Kumar, Santosh [1 ]
机构
[1] Banaras Hindu Univ, Inst Sci, Dept Math, Varanasi 221005, India
来源
关键词
Bertrand curve; Frenet frame; rectifying plane; osculating plane; normal plane; ruled surfaces; CURVATURE;
D O I
10.33039/ami.2022.12.011
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we introduce ruled like surfaces in three-dimensional Euclidean space, E3. To form a ruled like surface in E3, we consider a base curve gamma(s) and a director curve X(s). Let parameter s be the angle between the tangent of gamma(s) and X(s) when X(s) lie on rectifying plane or in the osculating plane. Whereas, if X(s) is in the normal plane, then parameter s will be the angle between the normal of gamma(s) and position vector of X(s) at the corresponding point in E3. Then we investigate some characterizations of such types of surfaces (say S(s, v)). Moreover, we find the condition for the existence of Bertrand mate of gamma(s) in S(s, v). Finally, as examples, we construct the surfaces S(s, v) by using a straight line, circle and helix in E3.
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页码:83 / 101
页数:19
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