Soley Ersoy

One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula

In [10] one-parameter planar motion was first introduced and the relations between absolute, relative, sliding velocities (and accelerations) in the Euclidean plane

Generalized spacelike Bertrand curves in Minkowski 5-space

{{\mathbb E}^2}

Bobillier Formula for the Elliptical Harmonic Motion

were obtained. Moreover, the relations between the complex velocities of one-parameter motion in the complex plane were provided by [10]. One-parameter planar homothetic motion was defined in the complex plane, [9]. In this paper, analogous to homothetic motion in the complex plane given by [9], one-parameter planar homothetic motion is defined in the hyperbolic plane. Some characteristic properties about the velocity vectors, the acceleration vectors and the pole curves are given. Moreover, in the case of homothetic scale h identically equal to 1, the results given in [15] are obtained as a special case. In addition, three hyperbolic planes, of which two are moving and the other one is fixed, are taken into consideration and a canonical relative system for one-parameter planar hyperbolic homothetic motion is defined. Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, is obtained with the help of this relative system.

On instantaneous invariants of hyperbolic planes

OnderGokmenYildizDepartment of Mathematics,Faculty of Arts and Sciences,Bilecik Seyh EdebaliUniversity,Bilecik/TURKEYogokmen.yildiz@bilecik.edu.trSoleyErsoyDepartment of Mathematics,Faculty of Arts and Sciences,Sakarya University,Sakarya/TURKEYsersoy@sakarya.edu.trMelek MasalDepartment of MathematicsTeaching,Faculty of Education,Sakarya University,Sakarya/TURKEYmmasal@sakarya.edu.trABSTRACTIn this paper, we investigate a general formulation for inextensible flows of curves onan oriented surface in R

On the Trajectory Null Scrolls in 3-Dimensional Minkowski Space-Time E 1 3

Abstract In this paper, we give the definition of the generalization of spacelike Bertrand curves and obtain the characterization of these curves in Minkowski 5-space . Moreover, we define three types special spacelike Bertrand curves in Minkowski 5-space

Rolling Circles of Motions: Yesterday and Today

In this paper, the definition of generalized spacelike Mannheim curve in Minkowski space-time

Timelike Tangent Developable Surfaces and Bonnet Surfaces

E_1^4

Elliptical Harmonic Motion and Euler–Savary Formula

is given. The necessary and sufficient conditions for the generalized spacelike Mannheim curve are obtained. Also, some characterizations of Mannheim curve are given.