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” …

In this paper, we investigate a curve whose spherical images (the tangent indicatrix and
binormal indicatrix) are spherical slant helices and called it as a C− slant helix. This notation …

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 …

In this paper, position vector of a slant helix with respect to standard frame in Euclidean
space E 3 is studied in terms of Frenet equations. First, a vector differential equation of third …

In this paper, for a given curve in the Euclidean 3-space R^3 we introduce new invariants
such as arc-length, curvature and torsion withfractional-order and provide certain relations …

In this work, the directional spherical indicatrices of a timelike space curve using tangent,
quasi-normal and quasi-binormal vectors with q-frame are introduced. Then we work on the …

In this paper, position vector of a time-like slant helix with respect to standard frame of
Minkowski space E31 is studied in terms of Frenet equations. First, a vector differential …

In this paper, we first introduce N-Bishop frame for a normal direction curve which is defined
as an integral curve of the principal normal of a curve. We express this new frame and its …

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In this paper, we introduce the notion of the principal (binormal)-directional curve and the
principal (binormal)-donor curve of the Frenet curve in the Minkowski space E13 …