  In this paper, we prove several Liouville-type theorems on the non-existence
of Killing-Yano tensors, Killing tensors, and harmonic symmetric tensors on
Hadamard manifolds and, in particular, on Riemannian symmetric spaces of
non-compact type. These theorems supplement the well-known vanishing theorems
for the above tensors, obtained using the Bochner technique for compact
Riemannian manifolds. In turn, the proofs of our theorems will use well-known
Liouville-type theorems on the non-existence of subharmonic and harmonic
functions on complete Riemannian manifolds, which we have partially modified
for the case of Hadamard manifolds and, in particular, Riemannian symmetric
spaces of noncompact type.
