Vanishing theorems for p-harmonic ℓ-forms on Riemannian manifolds with a weighted Poincaré inequality

Abstract

In this paper, we investigate p-harmonic ℓ-forms on Riemannian manifolds with a weighted Poincaré inequality, and we get a vanishing type theorem, which shows that if we put some assumptions on the bound of the Weitzenböck curvature operator and the first eigenvalue of the Laplacian operator, then there is no nontrivial p-harmonic ℓ-form (2≤ℓ≤n−2) with finite Lp norm on M, which generalizes the previous results of Vieira [20] and Dung [7]. Furthermore, we deduce some vanishing type theorems for p-harmonic 1-forms and L2 harmonic 1-forms on M.