On Vanishing Theorems for Locally Conformally Flat Riemannian Manifolds with an Integral Pinching Condition

In this paper, we show some vanishing theorems for harmonic p-forms on a locally conformally flat Riemannian manifold. In the concrete, provided that the integral of the traceless Ricci tensor has a suitable bound, we obtain a vanishing theorem for them without any scalar curvature conditions. Another theorem is also given under the condition on nonpositive scalar curvature, which improves and extends the ones previous.

Automated summary

In this paper, we investigate the vanishing theorems for harmonic p-forms on a locally conformally flat Riemannian manifold. Specifically, we present a vanishing theorem for them without the need for scalar curvature conditions, when the integral of the traceless Ricci tensor satisfies a suitable bound. Furthermore, we provide another theorem under the condition of nonpositive scalar curvature, which improves and extends previous results.