In this paper, we introduce a new frame which is called the B‐Darboux frame on a surface in
Euclidean 3‐space. We know that the parallel transport frame is derived from the Frenet …

In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an
oriented surface in the Galilean 3-dimensional space G3. These equations will give direct …

In this study, we define a variational field for constructing a family of Frenet curvesof the
length l lying on a connected oriented hypersurface and calculate the length of the …

In the present work, we study construction of offset surfaces with a givennon-null asymptotic
curve. Let $\alpha\left (s\right) $ be a spacelike ortimelike unit speed curve with non …

In this study, we worked on the second kind of relaxed elastic lines on dual spaces which
has an important point on kinematic. We also obtained boundary conditions for this type of …

Let 𝛼 be an arc on a connected oriented surface 𝑆 in Minkowski 3-space, parameterized by
arc length 𝑠, with torsion 𝜏 and length 𝑙. The total square torsion 𝐻 of 𝛼 is defined by H=∫ …

Abstract Theory of elasticity is a topic that keeps improving by using on many fields such as
geometry, physics, chemistry and engineering. Energy density is given as some functions of …

Let α (s) be an arc on a connected oriented surface S in E 3, parameterized by arc length s,
with torsion τ and length l. The total square torsion H of α is defined by H=∫ 0 l τ 2 ds. The …

In this study, we introduce a new frame on a surface, called as B-Darboux frame. It is well
known that we derive the parallel transport frame from the Frenet frame along a space curve …

In this purpose, we worked a new frame on a surface which called as B-Darboux frame in
Minkowski 3-space. The B-Darboux frame from the Darboux frame on a surface is derived in …