Harmonic maps of manifolds and general variational formula

This study consists of four chapters .in the first chapter,it is given an historical development of the classical harmonic functions up to harmonic morphisms and the relation between harmonic functions and complex analitical maps by the weiertrass representation.besides,it is shown that thecritical points of a smooth variational functional of the harmonic maps may define geodesic curves or minimal surfaces and furthermore in this chapter,it is given some fundamental concepts such as differentiable manifold, tensor fields,riemannian manifolds and the levicivita connection.in the second chapter,it is studied harmonic maps of the riemanian manifolds and defined the energy of a map and connections on a cotangent space and push -backed tangent fiber and so it is investigated the smooth variations of a map between two rienmannian manifolds.in the third chapter ,we state and prove the general version of the first variational formula for a smooth map between two riemannian manifolds.finally,the last chapter covers an evalution of the thesis.