Prolongations of hypersurfaces to vector bundles

In this thesis prolongations of hypersurfaces to vector bundles are studied andthe theory of hypersurfaces prolonged to the vector bundles are developed withrespect to the metric tensor which is the complete lift of the metric tensor of thebase space. Firstly, fundamental concepts required for the work are given.Secondly, a summary of the paper entitled ?Prolongations of hypersurfaces totangent budle? of M. Tani, which forms the framework of the thesis, is given. Inthe main part of thesis, firstly, the vertical and the complete lifts of the vectorfields defined along the hypersurface to vector bundle are defined. There after,the equation of Weingarten and the structure equations for the prolongedhypersurfaces are formulated in the form of lifts of the corresponding equationsof the hypersurface given in the base space. It was seen that of thesegeneralizations obtained in any vector bundle E coincide with earlier results ontangent bundle when TM tangent bundle is taken instead of the vector bundleE.Key Words : Hypersurface, prolongation, vector bundle