Geometrical structures on the tangent bundle

The differential geometry of tangent bundles was studied by several authorsamong others. It is well known that an almost complex structure defined on a differentiable manifold M of class C∞ can be lifted to the same type of structure on its tangent bundle T(M). However, when we consider an almost contact structure, we do not get the same type of structure on T(M). In this case we consider an odd dimensional base manifold while our tangent bundle remains to be even dimensional. The purpose of this paper is to examine certain structures on the base manifold M in relation to that of the tangent bundle T(M). In this book, we study the geometry fo the tangent bundle equipped with different types of structures, for this purpose we are first give some important definitions and well known results that are gonna be used in our study.