Title: Transverse Weitzenböck formulas and de Rham cohomology of totally geodesic foliations,
Abstract: We prove transverse Weitzenböck identities for the horizontal Laplacians of
a totally geodesic foliation. As a consequence, we obtain nullity theorems for
the de Rham cohomology assuming only the positivity of curvature quantities
transverse to the leaves. Those curvature quantities appear in the adiabatic
limit of the canonical variation of the metric.