On the structure of conformally flat Riemannian manifolds

In this paper we will prove vanishing and finiteness theorems for L2L2-harmonic 1-forms on a locally conformally flat Riemannian manifold which satisfies an integral pinching condition on the traceless Ricci tensor, and for which the scalar curvature is non-positive or satisfies some integral pinching conditions. Based on these vanishing and finiteness theorems, combining with the work of Li–Tam, we can obtain some one-end and finite ends theorems.