On the Spacelike Parallel Ruled Surfaces with Darboux Frame

In this study, the spacelike parallel ruled surfaces with Darboux frame are introduced in Minkowski 3-space. Then some characteristic properties of the spacelike parallel ruled surfaces with Darboux frame such as developability, the striction point and the distribution parameter are obtained in Minkowski 3-space

On curves of constant breadth in G¹₃

In this work, differential equations characterizing curves of constant breadth have been given in pseudo-Galilean space G¹₃. The special cases related to these differential equations have been studied in G¹₃.Publisher's Versio

TUBULAR SURFACES WITH DARBOUX FRAME IN GALILEAN 3-SPACE

In this paper, we define tubular surface by using a Darboux frame instead of a Frenet frame. Subsequently, we compute the Gaussian curvature and the mean curvature of the tubular surface with a Darboux frame. Moreover, we obtain some characterizations for special curves on this tubular surface in a Galilean 3-space

On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings

The trajectory of a robot end-effector is described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way, the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The curvature theory of a ruled surface generated by a line fixed in the end-effector referred to as the tool line is used for more accurate motion of a robot end-effector. In the present paper, we first defined tool trihedron in which tool line is contained for timelike ruled surface with timelike ruling, and transition relations among surface trihedron: tool trihedron, generator trihedron, natural trihedron, and Darboux vectors for each trihedron, were found. Then differential properties of robot end-effector's motion were obtained by using the curvature theory of timelike ruled surfaces with timelike ruling

On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings

The trajectory of a robot end-effector is described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way, the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The curvature theory of a ruled surface generated by a line fixed in the end-effector referred to as the tool line is used for more accurate motion of a robot end-effector. In the present paper, we first defined tool trihedron in which tool line is contained for timelike ruled surface with timelike ruling, and transition relations among surface trihedron: tool trihedron, generator trihedron, natural trihedron, and Darboux vectors for each trihedron, were found. Then differential properties of robot end-effector's motion were obtained by using the curvature theory of timelike ruled surfaces with timelike ruling

On the Curvatures of (k+1)-Dimensional Semi-Ruled Surfaces in ({{E}_{v}^{n+1} })

In this paper, first we will define the generalized (k + 1) -dimensional semi-ruled surface M*, such that the generator space of M* is the semi-subspace of E v n + 1 where E v n + 1 is the semi-Euclidean space. Then, we will compute the mean curvature, Riemann curvature, Ricci curvature and scalar curvature of M*

Some Relations Between The Integral Invariants Of A Closed Time-Like Ruled Surface

Bu çalışmada, Z)2 dual Lorentzian uzayında bir kapalı time-like regle yüzeyin bir dual integral invaryantı olan, dual açılım açısı kullanılarak, bir kapalı time-like regle yüzeyin doğal eğriliği, doğal burulması ve striksiyon büyüklükleri arasındaki bağıntılar elde edilmiştir. Bu bağıntılarla ilgili bazı sonuçlar verilmiştir.In this paper, using the dual angle of pitch which is a dual integral invariant of a closed time-like ruled surface in , Z)2 dual Lorentzian space, we obtained some relations between the quantities of natural curvature, natural torsion and striction of a closed time-like ruled surface. Some results are given about these relations

On the Darboux Vector of Ruled Surfaces in Pseudo-Galilean Space

In the Euclidean space the Darboux vector may be interpreted kinematically as the direction of the instantaneous axis of rotation in the moving trihedron. In this paper we mainly study the Darboux vector of ruled surfaces in pseudo-Galilean space. We obtain relationships between Darboux and Frenet vectors of each type of ruled surfaces in pseudo-Galilean space. Moreover we observe that in the pseudo-Galilean space the Darboux vector can be interpreted kinematically as a shear along the absolute line

A note on Berwald eikonal equation

International Conference on Quantum Science and Applications (ICQSA) -- MAY 25-27, 2016 -- Eskisehir Osmangazi University, Eskisehir, TURKEY -- Eskisehir Osmangazi Univ, Ctr Quantum Res & Applications, Eskisehir Osmangazi Univ (ESOGU)In this study, firstly, we generalize Berwald map by introducing the concept of a Riemannian map. After that we find Berwald eikonal equation through using the Berwald map. The eikonal equation of geometrical optic that examining light reflects, refracts at smooth, plane interfaces is obtained for Berwald condition.WOS:0004405153000292-s2.0-8499590020