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

Abstract

Abstract In this paper, we establish a finiteness theorem for L p $L^{p}$ 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. This result can be regarded as a generalization of Han’s result on L 2 $L^{2}$ harmonic 1-forms.

Keywords

• L p $L^{p}$ harmonic 1-forms
• Conformally flat
• Finite index