Biharmonic maps

In this thesis,there are five chapters. The first chapter is devoted to the introduction. Second chapter contains some well-known definitions and results which will be used in other chapters. Connections are studied in the third chapter. Harmonic and biharmonic maps between two Riemannian manifolds are introduced in section four. In section five, using the biharmonicity equation, it is found that a biharmonic hypersurface which has ∫_M▒〖‖H‖^2 v_g<∞〗condition in a Riemannian manifold of non-positive Ricci curvature is minimal, where H is the mean curvature of hypersurface. Then,biharmonicsubmersions which are a kind of biharmonic Riemannian maps are studied from a three-dimensional Riemannian manifold onto asurface.