L p $L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

In this paper, we establish a finiteness theorem for $L^{p}$ harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrodinger operators involving the squared norm of the traceless Ricci form. This result can be regarded as a generalization of Han’s result on $L^{2}$ harmonic 1-forms.