The Topological Structure of Conformally Flat Riemannian Manifolds

In this paper, we will prove vanishing and finiteness theorems for $L^2$-harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. From these theorems and the work of Li–Tam, we can obtain some one-end and finite ends results for the locally conformally flat Riemannian manifold.