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

Abstract

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.

Keywords

Harmonic p-form / Vanishing theorem / Locally conformally flat Riemannian manifold