Vanishing theorems of the basic harmonic forms on a complete foliated   Riemannian manifold
  On a compact foliated Riemannian manifold with some transversal curvature conditions, there are no nontrivial basic harmonic forms (M. Min-Oo et al., J. Reine Angew. Math. 415 (1991). In this paper, we extend the above facts to a complete foliated Riemannian manifold. 
Seoung Dal Jung and Huili Liu
math.DG