Conformal Killing L2-forms on complete Riemannian manifolds with nonpositive curvature operator

We give a classification for connected complete, locally irreducible Riemannian manifolds with nonpositive curvature operator, which admit a nonzero closed or co-closed conformal Killing L2-forms. In addition, we prove vanishing theorems for these forms on some complete Riemannian manifolds. Our proofs are based on the Bochner technique that is a most elegant and important analytical method in differential geometry “in the large”.