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 Schrödinger operators involving the squared norm of the traceless Ricci form. This result can be regarded as a generalization of Han’s result on $L^{2}$ harmonic 1-forms.

中文翻译：

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保形黎曼流形上的（（L ^ {p} \））调和1型

在本文中，我们在涉及无迹Ricci形式平方范式的Schrödinger算子的假设下，建立了局部保形平坦黎曼流形上$ L ^ {p} $调和1型的有限性定理。该结果可视为Han在$ L ^ {2} $调和1形式上的结果的推广。