A Liouvile-type theorems for some classes of complete Riemannian almost   product manifolds and for special mappings of complete Riemannian manifolds
  In the present paper we prove Liouville-type theorems: non-existence theorems for some complete Riemannian almost product manifolds and special mappings of complete Riemannian manifolds which generalize similar results for compact manifolds. 
Stepanov Sergey
math.DG