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

Abstract

In this paper, we obtain some vanishing and finiteness theorems for $L^{p}$ $p$-harmonic 1-forms on a locally conformally flat Riemmannian manifolds which satisfies an integral pinching condition on the traceless Ricci tensor, and for which the scalar curvature satisfies pinching curvature conditions or the first eigenvalue of the Laplace-Beltrami operator of $M$ is bounded by a suitable constant.