The bochner technique in riemannian geometry

In this thesis, the Bochner technique is presented in Riemannian geometry. Some basic concepts such as Riemannian metric tensor, Levi-Civita connection, tensor derivation, Riemannian curvature, Ricci curvature, scalar curvature used in Bochner technique are given. The Bochner formula is obtained. Some well-known theorems in Riemannian geometry are proved by use of this formula. These theorems include both the original Ricci curvature and a modification of its. Additionally, these theorems concern with harmonic vector field, Killing vector field and conformal Killing vector field. Hence, these vector fields are defined and their some properties are noted.