Prolongations of hypersurfaces to tangent bundles of order two

In this thesis, the theory of hypersurfaces that prolonged using metric tensor which is II lift of tangent bundles of order two of metric tensor of the base space is studied. Firstly, fundemental concepts used throughout the study is given. Secondly, the study of M. Tani entitled ?Prolongations of Hypersurfaces to Tangent Bundles? which constitutes the framework of the thesis is briefed. In the main part of the thesis, 0, I, II lifts to the second order tangent bundles defined over the hypersurfaces is obtained firstly. Then, making use of these lifts, the structure equations of the hypersurface which is prolonged using the structure equations of the given hypersurface in the base space is obtained.