Vanishing theorem for transverse Dirac operators on Riemannian foliations

We obtain a vanishing theorem for the half-kernel of a transverse Spin ^c Dirac operator on a compact manifold endowed with a transversely almost complex Riemannian foliation twisted by a sufficiently large power of a line bundle, whose curvature vanishes along the leaves and is transversely non-degenerate at any point of the ambient manifold.