Some structures with cheeger-gromoll metric on tangent bundles

In the introduction chapter of this thesis consisting of five chapters, some general evaluations have been done about the subject and some studies which are main into this subject have been given. In the second chapter, some fundamental notions which will be used in the original chapters of this thesis have been presented. In the third chapter, firstly the notion of natural metric has been determined on tangent bundles and some results have been given about it. Later, Cheeger-Gromoll (C-G) metric which is a type of the natural metrics on tangent bundles has been determined and some geometric results have been given about this metric. The fourth and fifth chapters of the thesis consist of the original studies. In the fourth chapter, firstly almost paracontact tangent bundles with C-G metric has been determined and then a theorem which characterizes the normality of these tangent bundles has been expressed. Also, paracontact, K-paracontact and para-Sasakian tangent bundles with C-G metric have been determined and some results have been obtained about these notions. In this chapter, finally some conclusions about the curvatures of almost paracontact tangent bundles with C-G metric have been given. In the fifth chapter, first the notion of metallic structure on a manifold M has been expressed and the notion of TM metallic structure on a tangent bundle TM have been determined. Later, a condition for a metallic tangent bundle which has been equipped with C-G metric to be a metallic Riemannian tangent bundle has been obtained. Finally, a theorem for a Golden Riemannian tangent bundle which is a class of the metallic Riemannian tangent bundles equipped with C-G metric to be locally decomposable has been given.