Transverse geometric formality

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.