General Rotational Surfaces with Pointwise 1-Type Gauss Map in Pseudo- Euclidean Space E42

In this paper, we study general rotational surfaces in the 4- dimensional pseudo-Euclidean space E4-2 and obtain a characterization of flat general rotation surfaces with pointwise 1-type Gauss map in E4-2 and give an example of such surfaces.Comment: arXiv admin note: substantial text overlap with arXiv:1302.280

A new approach on helices in pseudo-Riemannian manifolds

In this paper, we give a definition of harmonic curvature functions in terms of V_{n} and define a new kind of slant helix which is called V_{n}-slant helix in n-dimensional pseudo-Riemannian manifold. Also, we give important characterizations about the helix.Comment: arXiv admin note: substantial text overlap with arXiv:1305.704

One-parameter homothetic motion in the Minkowski 3-space

A one-parameter homothetic motion in three-dimensional Minkowski space is defined by means of the Hamilton operators. We study some properties of this motion and show that it has only one pole point at every instant t. We also obtain the Darboux vector of the homothetic motion in E³₁ and show that it can be written as multiplication of two split quaternions.Publisher's Versio

Dual split quaternions and Chasles’ theorem in 3-dimensional minkowski space E1_3

In 1831, Michel Chasles proved the existence of a fixed line under a general displacement in R3. The fixed line called the screw axis of displacement was obtained by McCharthy in [10]. The purpose of this paper is to develop the method which is given for the pure rotation in [14], and thus to obtain the screw axis of spatial displacement in 3- dimensional Minkowski space. Firstly, we give a relation between dual vectors and lines in E3_1, characterize the screw axis. Also, we discuss the dual split quaternion representation of a spatial displacement

Motion groups and circular helices in Lorentz 3-space

In this paper, we find the curves which are orbits of of points under the homothetic and helicoidal motion groups in Lorentz 3-space. Also, we show that if these curves are Frenet curves then their curvature and torsion are constant. So we can say that these curves are circular helix in Lorentz 3-space