  A Riemannian metric on a closed manifold is said to be geometrically formal
if the wedge product of any two harmonic forms is harmonic; equivalently, the
interior product of any two harmonic forms is harmonic. Given a Riemannian
foliation on a closed manifold, we say that a bundle-like metric is
transversely geometrically formal if the interior product of any two basic
harmonic forms is basic harmonic. In this paper, we examine the geometric and
topological consequences of this condition.
