  In this paper, we give a new lower bound for the eigenvalues of the Dirac
operator on a compact spin manifold. This estimate is motivated by the fact
that in its limiting case a skew-symmetric tensor (see Equation \eqref{eq:16})
appears that can be identified geometrically with the O'Neill tensor of a
Riemannian flow, carrying a transversal parallel spinor. The Heisenberg group
which is a fibration over the torus is an example of this case. Sasakian
manifolds are also considered as particular examples of Riemannian flows.
Finally, we characterize the 3-dimensional case by a solution of the Dirac
equation
