In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths,
geodesic curvatures according to the Lorentzian 3-space ℝ 3 1, Lorentzian sphere 𝕊 2 1 …

In this study, we compute the Frenet frame, the curvatures, the Frenet derivative formulas,
the Darboux vector, the arc length, the geodesic curvatures according to and (Lorentzian …

Adjoint curves of special Smarandache curves with respect to Bishop frame Page 1 AIMS
Mathematics, 9(12): 35355–35376. DOI: 10.3934/math.20241680 Received: 18 October 2024 …

The aim of this study is to examine Darboux frames and some other geometric properties
(geodesic curvatures, geodesic torsions, normal curvatures, Darboux derivative formulas …

In this paper, we obtain some characterizations of parallel curves of adjoint curves. In three-
dimensional Euclidean space, the relationship between [beta] adjoint of [alpha] curve and …

In this paper, we describe a new pair of curves where the principal normal vector of a curve
β and an vector R∗ lying in the rectifian plane of a curve β∗ are linearly dependent. We …

The aim of this study is to examine Darboux frames and some other geometric properties
(geodesic curvatures, geodesic torsions, normal curvatures, Darboux derivative formulas …

In this paper, we describe a new pair of curves where the principal normal vector of a curve
β and an vector R^* lying in the rectifian plane of a curve β^* are linearly dependent. We …

In this paper, we study tubular surfaces defined by adjoint curves which have a wide range
of applications. In three-dimensional Euclidean space, we consider tubular surfaces in …

This paper analyzes several specific ruled surfaces generated by the base curve α and its
director curve or the α's adjoint curve β and its director curve, where the director curves are …