Some vanishing theorems for p-harmonic l-forms on complete Riemannian manifolds

Abstract

In this paper, we give some vanishing theorems for p-harmonic l-forms on complete non-compact Riemannian manifolds. Firstly, we prove a vanishing theorem on Riemannian manifolds with nonnegative scalar curvature and a more general upper bound of pointwise curvature condition. Secondly, by using the similar trick, we obtain some vanishing theorems on complete immersed submanifold of Euclidean space.