Altunbas, Murat

Let (M, g) be a Riemannian manifold and (TM, ˜g) be its tangent bundle with the g−natural metric. In this paper, a family of metallic Riemannian structures J is constructed on TM, found conditions under which these structures are integrable. It is proved that (TM, ˜g, J) is decomposable if and only if (M, g) is flat.

Erişir, Tülay; İsabeyoğlu, Zeynep

In this paper, the spinor formulations of Mannheim curve pair are investigated. First of all, two spinors corresponding to Mannheim curve pair are given and considering the relationships between the Frenet frames of Mannheim curve pair the relationship between two spinors corresponding to this curve pair are obtained. Therefore, some geometric interpretations of spinors are obtained using the Mannheim curve pair and considering Mannheim curve as helix the spinor formulations of Mannheim curve pair are given. Moreover, the spinor formulations for the curvatures of the Mannheim curve pair are also obtained. Consequently, an example of these spinors is given. Therefore, it is thought that this study will make an important contribution to the mathematical analysis and geometric interpretation of spinors, which have many uses in physics.

Erisir, Tulay; Güngör, Mehmet Ali

In this paper, firstly, we calculate Cauchy-length formula for the one-parameter planar motion in generalized complex plane C-p which is generalization of the complex, dual and hyperbolic planes. Then, we give the length of the enveloping trajectories of lines C-p. In addition, we prove the Holditch theorem for the non-linear three points with the aid of the length of the enveloping trajectories in C-p. So, the Holditch theorem for the linear three points which is given by Erisir et al. in C-p is generalized for trajectories drawn by the non-linear three points in generalized complex plane C-p.

Gezer, Aydin; Bilen, Lokman; Karaman, Cagri; Altunbas, Murat

In this paper, we define a special new family of metrics which rescale the horizontal part by a nonzero differentiable function on the tangent bundle over a Riemannian manifold. We investigate curvature properties of the Levi-Civita connection and another metric connection of the new Riemannian metric.