In this work, we introduce a new version of Bishop frame using a common vector field as
binormal vector field of a regular curve and call this frame as “Type-2 Bishop Frame” …

We introduce the notion of the principal (binormal)-direction curve and principal (binormal)-
donor curve of a Frenet curve in E3 and give the relationship of curvature and torsion of its …

This paper presents a new approach of constructing special ruled surfaces and aims to
study their developability and minimalist conditions. Our concept opens opportunities for …

Daily-life foldable items, such as popup tents, the curved origami sculptures exhibited in the
Museum of Modern Art of New York, overstrained bicycle wheels, released bilayered …

In this paper, non-lightlike ruled surfaces of constant slope in Minkowski 3-space with a non-
lightlike base curve c (s)=∫ α t+ β n+ γ bds, where t, n, b are tangent, principal normal and …

In this article, a new approach is given for Bertrand curves in 3-dimensional Euclidean
space. According to this approach, the necessary and sufficient conditions including the …

In this paper, we consider the sequence of the principal‐directional curves of a curve γ and
define the slant helix of order n (n‐SLH) of the curve in Euclidean 3‐space. The notion is an …

In this study, original definitions of NC− Smarandache ruled surface and NW− Smarandache
ruled surface according to the alternative moving frame are introduced in E3. The main …

In this paper, firstly, we define a W-direction curve and W-rectifying curve of a Frenet curve in
3-dimensional Euclidean space E^ 3 by using the unit Darboux vector field W of the Frenet …

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