Ruled like surfaces in three dimensional Euclidean space
Buddhadev Pal, Santosh Kumar · Az Eszterházy Károly Tanárképző Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Az Eszterházy Károly Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Annales mathematicae et informaticae · 2023
In this paper, we introduce ruled like surfaces in three-dimensional Euclidean space, 𝐸 3 .To form a ruled like surface in 𝐸 3 , we consider a base curve 𝛾(𝑠) and a director curve 𝑋(𝑠).Let parameter 𝑠 be the angle between the tangent of 𝛾(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 𝛾(𝑠) and position vector of 𝑋(𝑠) at the corresponding point in 𝐸 3 .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 𝛾(𝑠) in S(𝑠, 𝑣).Finally, as examples, we construct the surfaces S(𝑠, 𝑣) by using a straight line, circle and helix in 𝐸 3 .